Answer
$\frac{y^2}{9}-x^2=1$
Work Step by Step
Transverse axis is vertical.
$(0,±a)=(0,±3)$
$a=3$
The equation of the asymptotes when transverse axis is vertical:
$y=±\frac{a}{b}x$
The equation of the asymptotes:
$y=±3x$
So:
$\frac{a}{b}=3$
$\frac{3}{b}=3$
$b=1$
Standard form when transverse axis is vertical:
$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$
$\frac{y^2}{3^2}-\frac{x^2}{1^2}=1$
$\frac{y^2}{9}-\frac{x^2}{1}=1$
$\frac{y^2}{9}-x^2=1$
