Answer
vertices $(0,-5),(0,5)$, foci $(0,-4),(0,4)$.
See graph.
Work Step by Step
1. Based on the given equation $\frac{x^2}{9}+\frac{y^2}{25}=1$, we have $a=5, b=3$ with center $(0,0)$ and a vertical major axis, thus $c=\sqrt {a^2-b^2}=\sqrt {25-9}=4$, vertices $(0,-5),(0,5)$, foci $(0,-4),(0,4)$.
2. See graph.
