Answer
asymptotes: $y=\pm\frac{5}{3}x$
foci: $(0, \pm\sqrt {34})$
Work Step by Step
Step 1. Rewriting the equation as $\frac{y^2}{25}-\frac{x^2}{9}=1$, we have $a=5, b=3, c=\sqrt {a^2+b^2}=\sqrt {34}$ centered at $(0,0)$ with a vertical transverse axis.
Step 2. We can find the vertices as $(0, \pm5)$ and asymptotes as $y=\frac{a}{b}x=\pm\frac{5}{3}x$
Step 3. We can graph the equation as shown in the figure with foci at $(0, \pm\sqrt {34})$
