Answer
$\frac{(x-3)^2}{9}+\frac{(y)^2}{36}=1$, foci: $(3,\pm3\sqrt {3})$.
Work Step by Step
Step 1. Rewrite the given equation as
$36(x^2-6x+9)+9(y^2)=324$
or
$\frac{(x-3)^2}{9}+\frac{(y)^2}{36}=1$,
Step 2. We have $a^2=36, b^2=9$ and $c=\sqrt {a^2-b^2}=3\sqrt {3}$. The ellipse is centered at $(3,0)$ with a vertical major axis.
Step 3. We can graph the equation as shown in the figure with foci at $(3,\pm3\sqrt {3})$.
