Answer
$\frac{(x+3)^2}{9}+\frac{(y-7)^2}{25}=1$
Work Step by Step
1. As the foci have the same x-coordinates, use the standard form $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$
2. The distance between the foci gives $2c=11-3=8$, thus $c=4$
3. The major axis of length gives $2a=10$, thus $a=5$
4. We have $b=\sqrt {a^2-c^2}=3$
5. The center can be found as $(-3, 7)$ from the foci
6. Thus the equation is $\frac{(x+3)^2}{9}+\frac{(y-7)^2}{25}=1$
