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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
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