Answer
$(x-0)^2=8(y-4)$
Work Step by Step
We are given that the directrix is below the given vertex, thus, $ p$ is the distance between the two points.
So, $p=4-2=2$
Since the directrix is horizontal, 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 $p$.
$(x-h)^2=4p(y-k)$
$\implies (x-0)^2=8(y-4)$
