Answer
$ \quad (x+1)^{2}+\displaystyle \frac{(y+1)^{2}}{4}=1$
Work Step by Step
1.$ \quad $Major axis: parallel to $y$ -axis$ \quad \Rightarrow \quad $(see table 3)
$ \displaystyle \frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1, \quad a \gt b \gt 0$
2.$ \quad $ Center: $(-1,-1)$
3.$ \quad 2a=4 \quad $ (Length of major axis)$ \quad a=2$
4.$ \quad 2b=1 \quad $ (Length of minor axis)$ \quad b=1$
Equation:$ \quad \displaystyle \frac{(x+1)^{2}}{1}+\frac{(y+1)^{2}}{4}=1$
or $ \quad (x+1)^{2}+\displaystyle \frac{(y+1)^{2}}{4}=1$
