Answer
center $(-5,4)$, foci $(-5-2\sqrt {3},4),(-5+2\sqrt {3},4)$, vertices $(-9,4),(-1,4)$
See graph.
Work Step by Step
1. Based on the given equation $\frac{(x+5)^2}{16}+\frac{(y-4)^2}{4}=1$, we can find center $(-5,4)$ with a horizontal major axis, $a=4, b=2$, $c=\sqrt {a^2-b^2}=\sqrt {16-4}=2\sqrt {3}$, thus foci $(-5\pm2\sqrt {3},4)$ or $(-5-2\sqrt {3},4),(-5+2\sqrt {3},4)$, vertices $(-5\pm4,4)$ or $(-9,4),(-1,4)$
2. See graph.
