Answer
See below
Work Step by Step
Rewrite the equation in standard form
$$\frac{y^2}{81}-\frac{x^2}{25}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=9$ and
$b=5$. The $y^2-term$ is positive, so the transverse axis is vertical and the vertices are at $(0,\pm 9)$. Find the foci:
$c^2=a^2+b^2=9^2+5^2=106\\
\rightarrow c=\sqrt 106$
The foci are at $(0,\pm \sqrt 106)$
The asymptotes are $y=\pm \frac{9}{5}x$
Draw the hyperbola.
