Answer
$\frac{y^2}{36}-\frac{x^2}{9}=1$
Work Step by Step
Step 1. From the given conditions, we have $a=6$ with a vertical transverse axis; thus the equation is in the form of $\frac{y^2}{36}-\frac{x^2}{b^2}=1$
Step 2. The asymptotes can be found as $y=\pm\frac{a}{b}x=\pm\frac{6}{b}x$. Comparing with the given asymptote, we have $\frac{6}{b}=2$, which gives $b=3$
Step 3. The equation is $\frac{y^2}{36}-\frac{x^2}{9}=1$
