Answer
$\frac{(x+1)^2}{4}+\frac{(y-1)^2}{1}=1$, foci $(-1\pm\sqrt 3,1)$
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 horizontal major axis.
Step 2. We can write the equation as $\frac{(x+1)^2}{4}+\frac{(y-1)^2}{1}=1$ with foci at $(-1\pm\sqrt 3,1)$
