Answer
$\frac{y^2}{36}-\frac{x^2}{20}=1$
Work Step by Step
Vertices: $(0,±a)=(0,±6)$
$a=6$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{6^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{36}-\frac{x^2}{b^2}=1$
The hyperbola passes through the point $(-5,9)$:
$\frac{9^2}{36}-\frac{(-5)^2}{b^2}=1$
$\frac{9}{4}-\frac{25}{b^2}=1$
$\frac{9}{4}-1=\frac{25}{b^2}$
$\frac{5}{4}=\frac{25}{b^2}$
$b^2=20$
Finally:
$\frac{y^2}{36}-\frac{x^2}{20}=1$
