Question

Answer the following:

Find the equation of the tangent to the parabola y² = 8x at t = 1 on it

Answer 1

Given equation of the parabola is y² = 8x

Comparing this equation with y² = 4ax, we get

4a = 8

∴ a = `8/4` = 2

t = 1

Equation of tangent with parameter t is

yt = x + at² 

∴ The equation of tangent with t = 1 is 

y(1) = x + 2(1)²

∴ y = x + 2

∴ x – y + 2 = 0