Question 1082287
The mid point between the two focus is the center of the ellipse.

In this case, Center= ((0+0)/2 , (2+-2)/2) =(0 , 0).

Let P = (3 , 2), F1 = (0 , -2), F2 =(0 , 2)

"The sum of the distance of a point of the ellipse to every Focus, is constant and equal to the double of the Semi-major axis (A)"

PF1 + PF2 = 2A.

5 + 3 = 2A

A = 4

Let C: distance from the center to a focus.

   C = 2.

A^2 = B^2 + C^2

   B = sqrt(12).

So the equation is

 x^2/12 + y^2/16 = 1.

observation: the Focus doesn't belong to the ellipse.

@natolino_