# How do you find the equation of a circle in standard form given #x^2+y^2+4x+6y+4=0#?

Please see the explanation.

The standard Cartesian form of the equation of a circle is:

Expand the squares:

The given equation is:

To make equation [3] look more like equation [2] group the x term together, group the y terms together and move the constant term to the right side:

To find the value of "h", set the second term of equation [2] equal to the second term of equation [5] and then solve for h:

To find the value of "k", set the fifth term of equation [2] equal to the fifth term of equation [5] and then solve for k:

Substitute -2 for h and -3 for k into equation [6]:

Combine the constants and write the constant as a square:

Equation [9] is in standard Cartesian form.

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To find the equation of a circle in standard form given the equation ( x^2 + y^2 + 4x + 6y + 4 = 0 ):

- Rearrange the given equation by completing the square for both the ( x ) and ( y ) terms.
- Complete the square for the ( x ) terms by adding ((4/2)^2 = 4) inside the parentheses.
- Complete the square for the ( y ) terms by adding ((6/2)^2 = 9) inside the parentheses.
- Rewrite the equation in standard form by grouping the squared terms together and isolating the constant term on one side.
- Write the equation in the standard form of a circle, which is ( (x - h)^2 + (y - k)^2 = r^2 ), where ( (h, k) ) is the center of the circle and ( r ) is the radius.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Points #(2 ,4 )# and #(4 ,9 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?
- Points #(6 ,7 )# and #(7 ,5 )# are #(2 pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
- Find the distance of the centre of the circle x^2+y^2+z^2+x-2y+2z=3,2x+y+2z=1 from the plane ax+by+cz=d, where a,b,c,d are constants.?
- A circle has a chord that goes from #( pi)/2 # to #(15 pi) / 8 # radians on the circle. If the area of the circle is #42 pi #, what is the length of the chord?
- What is the equation of the circle with a center at #(-1 ,-1 )# and a radius of #2 #?

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