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