Question

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

• A. $y = 0$
• B. $x = -1$
• C. $x = 0$
• D. $x - 1 = 0$

Answer 1

Answer: (C)

$x = 0$

Answer 2

Given, parametric equation of parabola is $x = t^2 + 1, y = 2t + 1$
$\Rightarrow x = \left(\frac{y -1}{2}\right)^{2} + 1$
$\Rightarrow \left(y - 1\right)^{2} =4\left(x-1\right)$
$\Rightarrow Y^{2} = 4X$
$\therefore$ Vertex is (1, 1), length of latus rectum = 4
Clearly, equation of directrix is
$X =- 1 \Rightarrow x-1 =-1\Rightarrow x=0$.