Answer
$x^2+\frac{y^2}{4}=1$, foci $(0,\pm\sqrt 3)$
Work Step by Step
Step 1. From the given graph, we can identify $a=2, b=1$; thus $c=\sqrt {a^2-b^2}=\sqrt {3}$. The ellipse is centered at $(0,0)$ with a vertical major axis.
Step 2. We can write the equation as $x^2+\frac{y^2}{4}=1$ with foci at $(0,\pm\sqrt 3)$
