Answer
See graph and explanations.
Work Step by Step
Step 1. Rewrite the given equation as $\frac{(x-1)^2}{4}+\frac{(y+3)^2}{9}=1$; we have $a^2=9, b^2=4$ and $c=\sqrt {a^2-b^2}=\sqrt 5$. The ellipse is centered at $(1,-3)$ with a vertical major axis.
Step 2. We can graph the equation as shown in the figure with foci at $(1,-3\pm\sqrt 5)$.
