Answer
See graph and explanations.
Work Step by Step
Step 1. Given $\frac{(x-3)^2}{9}+\frac{(y+1)^2}{16}=1$, we have $a^2=16, b^2=9$ and $c=\sqrt {a^2-b^2}=\sqrt 7$. The ellipse is centered at $(3,-1)$ with a vertical major axis.
Step 2. We can graph the equation as shown in the figure with foci at $(3,-1\pm\sqrt 7)$.
