Answer
$x^{2}=8y$
The latus rectum has endpoints $(-4,2)$ and $(4,2)$
Work Step by Step
Given: $a=2,\ (h,k)=(0,0)$
1. The focus and the vertex lie on the vertical line $\quad x=0.$
2. The focus $(0,2)$ is above the vertex $(0,0)$
So the parabola opens up.
3. By table 2, the equation is$\quad (x-h)^{2}=4a(y-k)$
that is, $\quad x^{2}=8y$
4. For $y=2, \quad x^{2}=16\Rightarrow x=\pm 4$
The latus rectum (line segment parallel to the directrix, containing the focus)
has endpoints $(-4,2)$ and $(4,2)$
5. Directrix: $\quad \quad y=k-a\quad \quad \Rightarrow\quad y=-2$
We have enough details for the graph.
