Find the equation of the tangent to the curve at x = 1 for the parametric equations below:

Question

Find the equation of the tangent to the curve at x = 1 for the parametric equations below:

x = e^t, y = (t - 1)²

A	y = 2x - 3
B	y = -2x - 3
C	y = -2x + 3
D	y = 2x + 3

Answer 1

If x = 1, then 1 = e^t, t = 0; dy/dx = (dy/dt)/(dx/dt) = 2(t - 1)/e^t; at t = 0 x = 1, y = 1, slope m = dy/dx = - 2.

Equation of tangent line y - 1 = - 2(x - 1); y = - 2x + 3

Answer is C: y = -2x + 3