Answer
See below
Work Step by Step
Given: $25y^2-64x^2=1600$
Rewrite the equation in standard form
$$\frac{y^2}{64}-\frac{x^2}{25}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=8$ and
$b=5$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,\pm 8)$. Find the foci:
$c^2=a^2+b^2=8^2+5^2=89\\
\rightarrow c=\sqrt 89$
The foci are at $(0,\pm \sqrt 89)$
The asymptotes are $y=\pm \frac{8}{5}x$
Draw the hyperbola.
