Question

The parametric equations of a parabola are x = t² + 1, y = 2t + 1. The cartesian equation of its directrix is 

विकल्प

• x = 0 

• x + 1 = 0 

• y = 0 

•  none of these 

Answer 1

 x = 0 

Given:
x = t² + 1         (1)
y = 2t + 1         (2)
From (1) and (2):

\[x = \left( \frac{y - 1}{2} \right)^2 + 1\] 

On simplifying: \[\left( y - 1 \right)^2 = 4\left( x - 1 \right)\] 

Let \[Y = y - 1 \text{ and } X = x - 1\]

∴ \[Y^2 = 4X\] 

Comparing it with y² = 4ax:
a = 1
Therefore, the equation of the directrix is X = −a , i.e.

\[x - 1 = - 1 \Rightarrow x = 0\]