Answer
$\frac{y^2}{144}-\frac{x^2}{25}=1$
Work Step by Step
Vertices: $(0,±a)=(0,±12)$
$a=12$
Foci: $(0,±c)=(0,±13)$
$c^2=a^2+b^2$
$b^2=c^2-a^2=13^2-12^2=169-144=25$
$b=5$
Asymptotes:
$y=±\frac{a}{b}x$
$y=±\frac{12}{5}x$
Hyperbola with vertical transverse axis:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{12^2}-\frac{x^2}{5^2}=1$
$\frac{y^2}{144}-\frac{x^2}{25}=1$
