Answer
See below
Work Step by Step
Given: $9y^2-25x^2=225$
Rewrite the equation in standard form
$$\frac{y^2}{25}-\frac{x^2}{9}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=5$ and
$b=3$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,\pm 5)$. Find the foci:
$c^2=a^2+b^2=5^2+3^2=34\\
\rightarrow c=\sqrt 34$
The foci are at $(0,\pm \sqrt 34)$
The asymptotes are $y=\pm \frac{5}{3}x$
Draw the hyperbola.
