Parabola 1 Question 9

9. The equation of the directrix of the parabola $y^{2}+4 y+4 x+2=0$ is

(2001, 1M)

(a) $x=-1$

(b) $x=1$

(c) $x=-3 / 2$

(d) $x=3 / 2$

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Answer:

Correct Answer: 9. (d)

Solution:

  1. Given,

$$ y^{2}+4 y+4 x+2=0 $$

$\Rightarrow$

$$ (y+2)^{2}+4 x-2=0 $$

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

Replace $\quad y+2=Y, x-\frac{1}{2}=X$

We have,

$$ Y^{2}=-4 X $$

This is a parabola with directrix at $X=1$

$$ \begin{array}{lc} \Rightarrow & x-\frac{1}{2}=1 \\ \Rightarrow & x=\frac{3}{2} \end{array} $$



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