Question

Question deleted.

Answer 1

Let z=p+qj
and the required ellipse be
(p/a)^2+(q/b)^2=1
then
|z+2|+|z-2|=6
The rules of conics tell us that c=2, a=6/2=3, and consequently b^2=(a^2-c^2)=5
So the required ellipse is
p^2/9+q^2/5=1