Answer
$\frac{(x+1)^2}{1}+\frac{(y+1)^2}{4}=1$, foci $(-1,-1\pm\sqrt 3)$
Work Step by Step
Step 1. From the given graph, we can identify $a=\frac{1-(-3)}{2}=2, b=1$. Thus $c=\sqrt {a^2-b^2}=\sqrt {3}$. The ellipse is centered at $(-1,-1)$ with a vertical major axis.
Step 2. We can write the equation as $\frac{(x+1)^2}{1}+\frac{(y+1)^2}{4}=1$ with foci at $(-1,-1\pm\sqrt 3)$
