Answer
$\frac{(x-4)^2}{5}+\frac{(y-6)^2}{9}=1$,
See graph.
Work Step by Step
1. Given vertices $(4,3)$ and $(4,9)$, focus $(4,8)$, we can identify a vertical major axis, center $(4,6)$ (midpoint of vertices), $a=9-6=3, c=8-6=2$, $b=\sqrt {a^2-c^2}=\sqrt {9-4}=\sqrt {5}$,
2. Thus we have $\frac{(x-4)^2}{5}+\frac{(y-6)^2}{9}=1$,
3. See graph.
