MCQ

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

#### Options

*x*= 0*x*+ 1 = 0*y*= 0none of these

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#### Solution

*x* = 0

Given:*x* = *t*^{2} + 1 (1)*y* = 2*t* + 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 y^{2} = 4ax:*a *= 1

Therefore, the equation of the directrix is *X = −a ,* i.e*. *

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

Is there an error in this question or solution?

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