Answer
$\frac{(x-2)^2}{25}+\frac{(y+1)^2}{9}=1$, see graph, foci $(6,-1)$ and $(-2,-1)$.
Work Step by Step
Step 1. Rewrite the given equation as $9(x^2-4x+4)+25(y^2+2y+1)=164+36+25=225$ or $\frac{(x-2)^2}{25}+\frac{(y+1)^2}{9}=1$,
Step 2. We have $a^2=25, b^2=9$ and $c=\sqrt {a^2-b^2}=4$. The ellipse is centered at $(2,-1)$ with a horizontal major axis.
Step 3. We can graph the equation as shown in the figure with foci at $(6,-1)$ and $(-2,-1)$.
