Answer
$\frac{(x-2)^2}{25}+\frac{(y+2)^2}{21}=1$,
See graph.
Work Step by Step
1. Given center $(2,-2)$, vertex $(7,-2)$, focus $(4,-2)$, we can identify a horizontal major axis, $a=7-2=5, c=4-2=2$, thus $b=\sqrt {a^2-c^2}=\sqrt {25-4}=\sqrt {21}$,
2. Thus we have $\frac{(x-2)^2}{25}+\frac{(y+2)^2}{21}=1$,
3. See graph.
