Answer
$\displaystyle \frac{x^{2}}{1}+\frac{y^{2}}{4}=1$
Foci: $(0, -\sqrt{3})$ and $(0, \sqrt{3})$.
Work Step by Step
The major axis is vertical (parallel to the y-axis). .
$\displaystyle \frac{(x-h)^{2}}{b^{2}}+ \displaystyle \frac{(y-k)^{2}}{a^{2}}=1$
From the graph,
$a=2,$
$b=1$,
center: $(0,0)$
$\displaystyle \frac{x^{2}}{1}+\frac{y^{2}}{4}=1$
Foci are $c$ units above and $c$ units below the center,
$c^{2}=a^{2}-b^{2}=4-1=3$
$c=\sqrt{3}$
The foci are at
$(0, -\sqrt{3})$ and $(0, \sqrt{3})$.
