Answer
asymptotes: $y= \pm\frac{5}{8}x$
foci: $(0, \pm\sqrt {89})$
Work Step by Step
Step 1. From the given equation $\frac{y^2}{25}-\frac{x^2}{64}=1$, we have $a=5, b=8, c=\sqrt {a^2+b^2}=\sqrt {89}$ centered at $(0,0)$ with a vertical transverse axis.
Step 2. We can find the vertices as $(0,\pm5)$ and asymptotes as $y=\frac{a}{b}x=\pm\frac{5}{8}x$
Step 3. We can graph the equation as shown in the figure with foci at $(0, \pm\sqrt {89})$
