Answer
The equation of the parabola is $$ y^{2}-4y-8x+4=0 $$
Work Step by Step
Given
Focus$
(2,2)$, Directrix $x=-2$
From the coordinates of the focus and Directix equation, we find the axis of the parabola is parallel to the $x-$ axis, opens rightward, and the vertex is $(0,2)$ and $p=2$
So, the general equation of the parabola is
$$ (y-k)^{2}=4 p(x-h) $$
So $(h,k)=(0,2)$
And
$$ (y-2)^{2}=4 (2)(x-0) $$
so we get $$ y^{2}-4y-8x+4=0 $$
