Question

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

• A. $ -1 $
• B. $ x=1 $
• C. $ x=-3/2 $
• D. $ x=3/2 $

Answer 1

Answer: (D)

Given equation can be rewritten as $ {{(y+2)}^{2}}=-4\left( x-\frac{1}{2} \right) $
$ \Rightarrow $ s $ {{Y}^{2}}=-4X, $
where $ Y=y+2 $ and $ X=x-\frac{1}{2} $ .
The equation of directrix is $ X=1 $ .
$ \therefore $ $ x-\frac{1}{2}=1\,\,\,\Rightarrow \,\,\,x=\frac{3}{2} $