Answer
$\frac{(x-2)^2}{5}+\frac{(y-2)^2}{9}=1$,
See graph.
Work Step by Step
1. Given vertices $(2,5)$ and $(2,-1)$, $c=2$, we can identify a vertical major axis, center $(2,2)$ (midpoint of vertices), $a=5-2=3, c=2$, $b=\sqrt {a^2-c^2}=\sqrt {9-4}=\sqrt {5}$,
2. Thus we have $\frac{(x-2)^2}{5}+\frac{(y-2)^2}{9}=1$,
3. See graph.
