Question

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

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

Answer 1

Answer: (D)

We can write the equation of the given parabola as $\left(y+2\right)^{2}=-4\left(x-\frac{1}{2}\right)$
Shifting the origin $(1/2, - 2)$, the equation of parabola becomes $Y^{2} = - 4X$, where $X = x - 1/2$, $Y - y + 2$.
The equation of its directrix is $X = 1$.
Hence, required equation of directrix is $x-\frac{1}{2}=1$ or $x=3/ 2$.