Answer
Foci: $(1, -3+\sqrt{5})$ and $(1, -3-\sqrt{5})$.
Work Step by Step
Bring to stadard form (divide with $36$)
$\displaystyle \frac{(x-1)^{2}}{4}+\frac{(y+3)^{2}}{9}=1$
(major axis vertical),
$a^{2}=9,$
$a=3$
$b^{2}=4$,
$b=2$
Center: $(1, -3)$
$c^{2}=a^{2}-b^{2}=9-4=5$
$ c=\sqrt{5}\approx$2.236
Foci are $c$ units above and $c$ units below the center.
Foci: $(1, -3+\sqrt{5})$ and $(1, -3-\sqrt{5})$.
