Question

Write an equation for each ellipse.

Short answer

The equation of ellipse is$\frac{{(x+1)}^2}{1}+\frac{{(y+1)}^2}{4}=1$

Step-by-step solution

Step 1. Given Information  

The given graph is

Step 2. Calculation 

The center of ellipse is at $(h,k)=(-1,-1)$. The vertices are $(-1,-3)and(-1,1)$.

Since, center and vertices all lie on the line localid="1647279150510" $x=-1$, the major axis is parallel to y-axis. The distance of center from each of the vertices is $a=2$.

The distance of center from x-intercept is $b=1$.

Substitute the values in the general form of equation.

$$\begin{gathered} \frac{{(x-h)}^2}{b^2}+\frac{{\left(y-k\right)}^2}{a^2}=1 \\ \frac{{(x+1)}^2}{1}+\frac{{(y+1)}^2}{4}=1 \end{gathered}$$