Answer
$\displaystyle y^2-\frac{x^{2}}{8}=1$
Work Step by Step
The foci have equal x-coordinates, the transverse axis is vertical so the equation is
$\displaystyle \frac{(y-k)^{2}}{a^{2}}- \displaystyle \frac{(x-h)^{2}}{b^{2}}=1$
The midpoint of the foci (the center): $(\displaystyle \frac{0+0}{2},\frac{-3+3}{2})=(0,0)$
The vertices are 1 unit above/below the center, so $a=1.$
$c^{2}=a^{2}+b^{2}$
$ c=3, a=1\Rightarrow b^{2}=3^{2}-1^{2}$
$b^{2}=8$
$\displaystyle \frac{y^{2}}{1^{2}}-\frac{x^{2}}{8}=1$
