Answer
Foci: $(4, 2)$ and $(4, -6)$.
Work Step by Step
$\displaystyle \frac{(x-4)^{2}}{25}+\frac{(y+2)^{2}}{5}=1$
(major axis horizontal),
$a^{2}=25,$
$a=5$
$b^{2}=9$,
$b=3$
Center: $(h,k)=(4,-2)$
$c^{2}=a^{2}-b^{2}=25-9=16$
$c=4$
Foci are $c$ units above and $c$ units below the center.
Foci: $(4, 2)$ and $(4, -6)$.
