ANSWER:
[tex]\frac{(x+2)^2\: }{4}+\frac{(y-2)^2}{9}=1[/tex]
STEP-BY-STEP EXPLANATION:
The general equation of an ellipse with no center at the origin is:
[tex]\frac{\mleft(x-h\mright)^2\: }{\: a^2}+\frac{\mleft(y-k\mright)^2}{b^2}=1[/tex]
Where (h, k) is the center of the ellipse, a is the distance from the center to the edge horizontally, and b is the distance from the center to the edge vertically.
From the graph we obtain these values, just like this:
Therefore, the equation is:
[tex]\begin{gathered} \frac{\mleft(x-(-2)\mright)^2\: }{\: 2^2}+\frac{\left(y-2\right)^2}{3^2}=1 \\ \frac{\mleft(x+2\mright)^2}{4}+\frac{\mleft(y-2\mright)^2}{9}=1 \end{gathered}[/tex]
