Answer
center $(-4,-2)$, foci $(-4-\sqrt {5},-2),(-4+\sqrt {5},-2)$, vertices $(-7,-2),(-1,-2)$
See graph.
Work Step by Step
1. Based on the given equation $\frac{(x+4)^2}{9}+\frac{(y+2)^2}{4}=1$, we can find center $(-4,-2)$ with a horizontal major axis, $a=3, b=2$, $c=\sqrt {a^2-b^2}=\sqrt {9-4}=\sqrt {5}$, thus foci $(-4\pm\sqrt {5},-2)$ or $(-4-\sqrt {5},-2),(-4+\sqrt {5},-2)$, vertices $(-4\pm3,-2)$ or $(-7,-2),(-1,-2)$
2. See graph.
