Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the equation as shown in the figure.
Step 2. Rewrite the equation as $x^2-4x+4 +9(y^2+6y+9) =4+81-49$ or $(x-2)^2+9(y+3)^2)=36$, which gives $\frac{(x-2)^2}{36}+\frac{(y+3)^2}{4}=1$; thus $a=6, b=2$, and $c=\sqrt {6^2-2^2}=4\sqrt {2}$
Step 3. As the center of the ellipse is at $(2,-3)$ and the major axis is horizontal, the foci are $(2-4\sqrt 2,-3)$ and $(2+4\sqrt 2,-3)$ as shown in the figure.
