Answer
Equation of parabola is $(x -2)^2 = 2(y +2)$.
Focus: $(2,-\frac{3}{2})$
Directrix : $y=-\frac{5}{2}$
Work Step by Step
If a parabola is oriented upwards, the equation of the parabola is,
$(x -h)^2 = 4p(y - k)$.
However, if a parabola is oriented laterally, the equation of the parabola is, $(y -h)^2 = 4p(x - k)$. In the equation, the vertex of the parabola is at $(h, k)\ or\ (k,h)$ respectively.
The focus is at $(h, k + p)\ or\ (k+p,h)$, respectively.
So let us plug in our given points.
Vertex: $(2,-2)$
Hence, $p=\frac{1}{2}$
Equation of parabola is $(x -2)^2 = 2(y +2)$.
Focus: $(2,-\frac{3}{2})$
Directrix : $y=-\frac{5}{2}$
