Answer
Center $ \quad (3,-1)$
Foci: $ \quad (3,-1+\sqrt{5}),\quad (3,-1-\sqrt{5})$
Vertices: $ \quad (3,2),\quad (3,-4)$
Work Step by Step
The form of the equation is
$ \displaystyle \frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1, \quad a \gt b \gt 0$.
1. $ \quad $The main axis is vertical,
2. $ \quad $Center = $(3,-1)$,
3.$ \quad a=3, b=2.$
Find $c: $
$c^{2}=a^{2}-b^{2}=9-4=5$
$c=\sqrt{5}\approx 2.236$
Vertices: $ \quad (h,k\pm a)=(3,-1\pm 3)$
$(3,2),\quad (3,-4)$
Foci: $ \quad (h,k\pm c) = (3,-1\pm\sqrt{5})$
