Q81 / 200 · Manipal (MET) 2012 · Mathematics
The equation of directrix of the parabola $y^2+4 y+4 x+2=0$ is
- A$x=-1$
- B$x=1$
- C$x=-\frac{3}{2}$
- Correct answerD$x=\frac{3}{2}$
Solution
We have, $y^2+4 y+4 x+2=0$
$\begin{aligned}
\Rightarrow & (y+2)^2+4 x-2 & =0 \\
\Rightarrow & (y+2)^2 & =-4\left(x-\frac{1}{2}\right)
\end{aligned}$
Replace, $\quad y+2=Y, x-\frac{1}{2}=X$
We have, $\quad Y^2=-4 X$
This is a parabola with directrix at $X=1$
$\begin{array}{lr}
\Rightarrow & x-\frac{1}{2}=1 \\
\Rightarrow & x=\frac{3}{2}
\end{array}$
Hence, the correct answer is option: 'D'.