The length of the axis are as follows:

Between : length is 6-(-2)=8

Between : length is 5-1=4

So it follows that the major axis is parallel to the x axis and , and the minor axis is parallel to the y axis and .

The ellipse will take the form .

I leave it for you to verify that the center of the ellipse is (2,3).

Therefore, the equation of the ellipse is

Does this make sense?