How do you convert the parametric equations into a Cartesian equation by eliminating the parameter r: #x=(r^2)+r#, #y=(r^2)-r#?

We have:

Adding the equations:

Multiplying the Equations we get:

Thus the Cartesian equation is:

We have:

Summing the equations we have:

and subtracting the second from the first:

or:

Then:

and finally:

This is the equation of a conic, so we can calculate the invariants:

The cubic invariant is non null so the conic is non-degenerate,

the quadratic invariant is null so the conic is a parabola.

graph{x^2+y^2-2xy-2x-2y=0 [-213.9, 213.8, -106.2, 107.5]}

To eliminate the parameter ( r ) and convert the parametricTo eliminate the parameter ( r ) and convert the parametric equationsTo eliminate the parameter ( r ) and convert the parametric equations (To eliminate the parameter ( r ) and convert the parametric equations ( xTo eliminate the parameter ( r ) and convert the parametric equations ( x =To eliminate the parameter ( r ) and convert the parametric equations ( x = rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 -To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into aTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a CartesianTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation,To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, youTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you canTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solveTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve forTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) inTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in oneTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation andTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substituteTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute itTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve oneTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it intoTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation forTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the otherTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) andTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and thenTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substituteTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From theTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it intoTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

2. From the firstTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into theTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

3. From the first equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the otherTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

4. From the first equation (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

5. From the first equation ( xTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

FirstTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First,To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( xTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) forTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \fracTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrtTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formulaTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. SubstituteTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute thisTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expressionTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \fracTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression forTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-bTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pmTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) intoTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrtTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into theTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the secondTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{bTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

whereTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( yTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ),To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \leftTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( bTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left(To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \fracTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ),To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), andTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrtTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( cTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2}To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \rightTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \fracTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 -To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

SubTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

SubstituteTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute (To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r )To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 +To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( yTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = rTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4xTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2}To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ yTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y =To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left(To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. SimplTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \fracTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. SimplifyTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify thisTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation toTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \rightTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to getTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to get theTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^2To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to get the CartesianTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^2 -To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to get the Cartesian equationTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^2 - \To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to get the Cartesian equation.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^2 - \leftTo eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve for ( r ) in one equation and substitute it into the other equation.

1. From the first equation ( x = r^2 + r ), solve for ( r ):

[ r = \frac{-1 + \sqrt{1 + 4x}}{2} ]

2. Substitute this expression for ( r ) into the second equation ( y = r^2 - r ):

[ y = \left( \frac{-1 + \sqrt{1 + 4x}}{2} \right)^2 - \frac{-1 + \sqrt{1 + 4x}}{2} ]

3. Simplify this equation to get the Cartesian equation.To eliminate the parameter ( r ) and convert the parametric equations ( x = r^2 + r ) and ( y = r^2 - r ) into a Cartesian equation, you can solve one equation for ( r ) and then substitute it into the other equation.

First, solve ( x = r^2 + r ) for ( r ):

[ r^2 + r - x = 0 ]

Using the quadratic formula:

[ r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

where ( a = 1 ), ( b = 1 ), and ( c = -x ), you get:

[ r = \frac{-1 \pm \sqrt{1 + 4x}}{2} ]

Substitute ( r ) into ( y = r^2 - r ):

[ y = \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right)^2 - \left( \frac{-1 \pm \sqrt{1 + 4x}}{2} \right) ]

After simplification, you will obtain the Cartesian equation in terms of ( x ) and ( y ).