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