Elliptic trajectory is a set of points whose sum of distances from points to two focal points is constant.

So the equation is

√((x-0)^2+(y+2)^2)+√((x-0)^2+(y-2)^2)= √((3/2)^2+(9/2)^2)+√((3/2)^2+( 1/2)^2)

Square, shift term, quadratic, elliptic equation is:

5x？ + 3y？ = 30

Or standard x? /6 + y？ / 10 = 1