Answer
vertices $(-5,0),(5,0)$, foci $(-\sqrt {21},0),(\sqrt {21},0)$.
See graph.
Work Step by Step
1. Based on the given equation $\frac{x^2}{25}+\frac{y^2}{4}=1$, we have $a=5, b=2$ with center $(0,0)$ and a horizontal major axis, thus $c=\sqrt {a^2-b^2}=\sqrt {25-4}=\sqrt {21}$, vertices $(-5,0),(5,0)$, foci $(-\sqrt {21},0),(\sqrt {21},0)$.
2. See graph.
