Answer
$x^2 = -12(y-3)$
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. (Definition, p.695). The focus is at $(h, k + p)$ or $(k+p,h)$, respectively. So let us plug in our given points. The parabola is vertically oriented since the focus is below the vertex. The focus is equidistant from the vertex as the vertex is from the directrix. Thus the focus is $(0,0)$ and the vertex is $(0,3)$. Thus, $h=0$ and $k=3$ and $p=-3$. Thus the equation is $(x -0)^2 = 4(-3)(y -3)$ or $x^2 = -12(y-3)$.
