Answer
$\frac{(x-2)^2}{16}+\frac{(y-1)^2}{7}=1$,
See graph.
Work Step by Step
1. Given foci $(5,1)$ and $(-1,1)$, $2a=8$, we can identify a horizontal major axis, center $(2,1)$ (midpoint of foci), $a=4, c=5-2=3$, $b=\sqrt {a^2-c^2}=\sqrt {16-9}=\sqrt {7}$,
2. Thus we have $\frac{(x-2)^2}{16}+\frac{(y-1)^2}{7}=1$,
3. See graph.
