Answer
Foci:
$(1-\sqrt{7}, -2)$ and $(1+\sqrt{7},-2)$.
Work Step by Step
$16 > 9$ so the major axis is horizontal.
Comparing with
$\displaystyle \frac{(x-h)^{2}}{a^{2}}+ \displaystyle \frac{(y-k)^{2}}{b^{2}}=1$,
$a=4,$
$b=3$
Center: $(h,k)= (1, -2)$
Vertices: $(h-a, k),\quad (h+a, k) $
$(1-4, -2),\quad (1+4, -2)$
$(-3, -2),\quad (5, -2) $
Foci are $c$ units right and $c$ units left of center,
$c^{2}=a^{2}-b^{2}16-9=7$
$c=\sqrt{7}\approx 2.65$
Foci:
$(1-\sqrt{7}, -2)$ and $(1+\sqrt{7},-2)$.
