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