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

a) x=0 b)x+1=0 c)y=0 d) none of these

It is given that* *

*x* = *t*^{2} +1 ...(1)

*y* = 2*t* + 1 ...(2)

From (1) and (2), we get

(*y *– 1)^{2 }= 4 (*x* – 1) ...(3)

Let *Y* = *y *– 1 and *X* = *x* – 1

Then

(3) ⇒ *Y*^{2}* = *4*X*

Equation of the directrix for parabola *Y*^{2}* = *4*X *is:

*X = *–1

⇒ *x* – 1 *= *–1

⇒ *x* = 0

This is the required equation of directirx.

Thus, the correct answer is **a**.

**
**