Answer
$\frac{(x-1)^2}{16}+\frac{(y+2)^2}{9}=1$, foci at $(1\pm\sqrt 7,-2)$.
Work Step by Step
Step 1. Rewrite the given equation as
$9(x^2-2x+1)+16(y^2+4y+4)=71+9+64=144$
or
$\frac{(x-1)^2}{16}+\frac{(y+2)^2}{9}=1$,
Step 2. We have $a^2=16, b^2=9$ and $c=\sqrt {a^2-b^2}=\sqrt 7$. The ellipse is centered at $(1,-2)$ with a horizontal major axis.
Step 3. We can graph the equation as shown in the figure with foci at $(1\pm\sqrt 7,-2)$.
