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

y = 0

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x = - 1

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x = 0

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x - 1 = 0

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Solution

The correct option is B $x = 0$
We have, $x = t^{2} + 1 \Rightarrow x - 1 = t^{2}$

And $y = 2 t + 1 \Rightarrow y - 1 = 2 t$

Now $(y - 1)^{2} = 4 t^{2} = 4 (x - 1)$

$\Rightarrow (y - 1)^{2} = 4 (x - 1)$

By comparing

$a = 1$

So the directrix is, $x - 1 = - a$

$\Rightarrow x = 0$

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

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