Chapter 9 - Section 9.2 - The Hyperbola - Exercise Set - Page 981: 6

$\dfrac{y^2}{4}-\dfrac{x^2}{32}=1$

Foci: $(0,-6), (0,6)$ and Vertices: $(0,2)$ and $(0,-2)$ We are given that $ c=6; a=2$ Since $ c^2=a^2+b^2$ so, $ b^2=c^2-a^2=36-4=32$ Thus, the equation for the hyperbola is: $\dfrac{y^2}{4}-\dfrac{x^2}{32}=1$