Answer
Foci: $(3, -1+\sqrt{7})$ and $(3, -1-\sqrt{7})$.
Work Step by Step
$\displaystyle \frac{(x-3)^{2}}{9}+\frac{(y+1)^{2}}{16}=1$
(major axis vertical),
$a^{2}=16,$
$a=4$
$b^{2}=9$,
$b=3$
Center: $(h,k)=(3, -1)$
$c^{2}=a^{2}-b^{2}=16-9=7,$
$c=\sqrt{7}\approx 2.646$
Foci are $c$ units above and $c$ units below the center.
Foci: $(3, -1+\sqrt{7})$ and $(3, -1-\sqrt{7})$.
