Answer
$\frac{(x)^2}{25}+\frac{(y-6)^2}{16}=1$, foci: $(\pm3,6)$.
Work Step by Step
Step 1. Rewrite the given equation as
$16(x^2)+25(y^2-12y+36)=25(36)-500=400$
or
$\frac{(x)^2}{25}+\frac{(y-6)^2}{16}=1$,
Step 2. We have $a^2=25, b^2=16$ and $c=\sqrt {a^2-b^2}=3$. The ellipse is centered at $(0,6)$ with a horizontal major axis.
Step 3. We can graph the equation as shown in the figure with foci at $(\pm3,6)$.
