Answer
See graph and explanations.
Work Step by Step
Step 1. Given $\frac{(x-4)^2}{9}+\frac{(y+2)^2}{25}=1$, we have $a^2=25, b^2=9$ and $c=\sqrt {a^2-b^2}=4$. The ellipse is centered at $(4,-2)$ with a vertical major axis.
Step 2. We can graph the equation as shown in the figure with foci at $(4,-6)$ and $(4,2)$
