Answer
$\frac{y^2}{4}-\frac{x^2}{32}=1$
Work Step by Step
Transverse axis is vertical.
$(0,±a)=(0,±2)$
$a=2$
$(0,±c)=(0,±6)$
$c=6$
$b^2=c^2-a^2=36-4=32$
$b=4\sqrt 2$
Standard form when transverse axis is vertical:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{2^2}-\frac{x^2}{(4\sqrt 2)^2}=1$
$\frac{y^2}{4}-\frac{x^2}{32}=1$
