Answer
See below
Work Step by Step
The standard form for a hyperbola with a vertical transverse axis: $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
We can see that the foci lie on the y-axis, so the transverse axis is vertical.
The vertices are 6 units from the center, so $a=6$
The foci are 9 units from the center so $c=9$
Find b: $b^2=c^2-a^2\\=9^2-6^2\\=45$
Plug in the values: $\frac{y^2}{36}-\frac{x^2}{45}=1$
