Question

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

• A. $x=-1$
• B. $x=1$
• C. $x=-\frac{3}{2}$
• D. $x=\frac{3}{2}$

Answer 1

The correct option is D $x=\frac{3}{2}$

$y^2+4y+4x+2=0$
$\Rightarrow (y+2{)}^2+4x-2=0$
$\Rightarrow (y+2{)}^2=-4(x-\frac{1}{2})$
Replace $y+2=Y,x-\frac{1}{2}=X$
We have, $Y^2=-4X$
This is a parabola with directrix at X =1
$\Rightarrow x-\frac{1}{2}=1$
$\Rightarrow x=\frac{3}{2}$