Question

The equation of the parabola with vertex at the origin and directrix $y = 2$ is

• A. $y^{2} = 8x$
• B. $y^{2} = - 8x$
• C. $y^{2}=\sqrt{8}\, x$
• D. $x^{2} = - 8 y$

Answer 1

Answer: (D)

Since directrix of parabolais $y = 2$
$\Rightarrow \, y-2=0$

So, vertex of parabola is $\left(0, 0\right)$ and focus $S$ is $\left(0, -2\right)$. So, equation of parabola will be $x^{2} = - 4 ay$
$\Rightarrow \, x^{2} = - 4 \times 2 y = - 8 y$.