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