Answer
$(x+1)^2+\frac{(y+1)^2}{4}=1$
Work Step by Step
The ellipse has a major axis parallel to the y-axis, hence the equation of the ellipse here has the form $\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1$, where $a\gt b\gt0$ and $(h,k)$ is the center.
$(h,k)=(-1,-1)$, $a=2$, $b=1$, hence the equation is: $\frac{(x-(-1))^2}{1^2}+\frac{(y-(-1))^2}{2^2}=1\\(x+1)^2+\frac{(y+1)^2}{4}=1$
