Answer
See below
Work Step by Step
Rewrite the equation in standard form
$$\frac{x^2}{9}-\frac{y^2}{36}=1$$
The denominator of $x^2$ is bigger than $y^2$, so the transverse axis is horizontal.
Identify the vertices, foci, and asymptotes. Note that $a=3$ and
$b=6$. The $y^2-term$ is positive, so the transverse axis is vertical and the vertices are at $(\pm 3,0)$. Find the foci:
$c^2=a^2+b^2=3^2+6^2=45\\
\rightarrow c=3\sqrt 5$
The foci are at $(\pm 3\sqrt 5,0)$
The asymptotes are $y=\pm 2x$
Draw the hyperbola.
