Answer
$(x-0)^2=-8(y-2)$ or, $x^2=-8(y-2)$
Work Step by Step
We are given that the focus is above the given diretcrix; thus, $ p$ is the negative of half of the distance between the two points.
So, $p=\dfrac{-1}{2}|4-0|=-2$
Since the vertex and focus have the same x-coordinate, the parabola must have a vertical axis.
Now, we will write the equation for the parabola that has a vertical axis using the vertex and $p$.
$(x-h)^2=4p(y-k)$
$\implies (x-0)^2=-8(y-2)$ or, $x^2=-8(y-2)$
