How do you find the equations of the tangents to that curve #x=3t^2 + 1# and #y=2t^3 + 1# that pass through point (4,3)?
Tangent Line
We find the equation first consisting only of x and y by eliminating variable t.
Use the first equation then substitute its equivalent in the second equation
God bless...I hope the explanation is useful.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the equations of the tangents to the curve (x = 3t^2 + 1) and (y = 2t^3 + 1) that pass through the point ((4,3)), we follow these steps:

First, we differentiate both equations with respect to (t) to find expressions for (\frac{dy}{dx}).

Then, we find the value of (t) that corresponds to the point of tangency by substituting (x = 4) and (y = 3) into the parametric equations.

Next, we find the slope of the tangent line at that point by substituting the (t) value into the expression for (\frac{dy}{dx}).

After obtaining the slope, we use the pointslope form of the equation of a line to find the equations of the tangents.
By following these steps, we can determine the equations of the tangents to the given curve that pass through the point ((4,3)).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 For #f(t)= (t^2,t^3)# what is the distance between #f(1)# and #f(3)#?
 How do you find the parametric equations for a line segment?
 How do you convert each parametric equation to rectangular form: x = t  3, y = 2t + 4?
 For #f(t)= (cos2t,sin^2t)# what is the distance between #f(pi/4)# and #f(pi)#?
 For #f(t)= (lnte^t, t^2/e^t)# what is the distance between #f(2)# and #f(4)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7