Question

If the equation of directrix of the parabola $y^2+4y+4x+2=0$ is $x=\frac{p}{q},$ where $p$ and $q$ are co-prime, then the value of $pq$ is

Answer 1

Given : $y^2+4x+4y+2=0$
$\Rightarrow y^2+4y+4=-4x+2$
$\Rightarrow (y+2{)}^2=-4(x-\frac{1}{2})$
Comparing with $Y^2=-4AX$ whose directrix is given by $X=A$
$\therefore$ Required equation of directrix is $x-\frac{1}{2}=1$
$\Rightarrow x=\frac{3}{2}$
$\therefore pq=6$