The parametric equations of a parabola are x=t^2 +1, y= 2t+1. The Cartesian equation of its directrix is

Question

The parametric equations of a parabola are x=t^2 +1, y= 2t+1. What is the Cartesian equation of its directrix?

Answer 1

It is given that 

x = t² +1 ...(1)

y = 2t + 1 ...(2)

From (1) and (2), we get

(y – 1)² = 4 (x – 1) ...(3)

Let Y = y – 1 and  X = x – 1

Then from equation (3) we have

⇒ Y² = 4X

Equation of the directrix for parabola Y² = 4X is:

X = –1

⇒ x – 1 = –1

⇒ x = 0

This is the required equation of directrix.