The equation of an ellipse in standard form follows:

$$\frac{(x-h{)}^2}{a^2}+\frac{(y-k{)}^2}{b^2}=1$$

To find the center of the ellipse:

The x coordinate of the center will be the same as (2,2) and (2,-8), 2, which makes h = 2;

The x coordinate of the center will be the same as (-1,-3) and (5,-3), -3, which makes k = -3;

The center is (2,-3).

The distance between the center (2,-3) and (5,-3) is 5-2=3, which makes a = 3;

The distance between the center (2,-3) and (2,2) is 2-(-3)=5, which makes b = 5;

Therefore the ellipse equation is:

$$\frac{(x-2{)}^2}{3^2}+\frac{(y+3{)}^2}{5^2}=1$$

$$=>\frac{(x-2{)}^2}{9}+\frac{(y+3{)}^2}{25}=1$$