Answer
$\frac{(x+1)^2}{16}+\frac{(y-2)^2}{49}=1$, foci: $(-1,2\pm\sqrt {33})$.
Work Step by Step
Step 1. Rewrite the given equation as
$49(x^2+2x+1)+16(y^2-4y+4)=671+49+64=784$
or
$\frac{(x+1)^2}{16}+\frac{(y-2)^2}{49}=1$,
Step 2. We have $a^2=49, b^2=16$ and $c=\sqrt {a^2-b^2}=\sqrt {33}$. The ellipse is centered at $(-1,2)$ with a vertical major axis.
Step 3. We can graph the equation as shown in the figure with foci at $(-1,2\pm\sqrt {33})$.
