Answer
$$\Rightarrow \frac{y^{2}}{36}-\dfrac {x^{2}}{324}=1$$
Work Step by Step
Equation of hyperbola with a format of
$$\dfrac {y^{2}}{a^{2}}-\dfrac {x^{2}}{b^{2}}=1\left( a > 0,b > 0\right) $$
Vertices are $\left( 0,\pm a\right) $
Asymptotes are $y=\pm \dfrac {a}{b}x$
Given vertices $(0,\pm6)$ we find $a=6$ and given asymptotes $(\pm\frac{1}{3}x)$ we find $\dfrac{a}{b}=\frac{1}{3}$
$\Rightarrow b=18$
Then the equation will be
$$\Rightarrow \frac{y^{2}}{36}-\dfrac {x^{2}}{324}=1$$
