Let point P(x,y) so, √(x−1)2+(y+1)2+√(x+1)2+(y−1)2=4 (x−1)2+(y+1)2+(x+1)2+(y−1)2=16 2(x2+y2+2)+2√(x−1)2+(y+1)2√(x+1)2+(y−1)2=16 (x2+y2+2)+√(x−1)2+(y+1)2√(x+1)2+(y−1)2=8 Then, [(x−1)2+(y+1)2][(x+1)2+(y−1)2]=(6−x2−y2)2 [x2+y2−2x+2y+2][x2+y2+2x−2y+2]=(x2+y2−6)2 (x2+y2+2)2−4(x−y)2=(x2+y2−6)2 [(x2+y2+2)−(x2+y2−6)][(x2+y2+2)+(x2+y2−6)]=4(x−y)2 Further simplify the above, 8(2x2+2y2−4)=4(x2+y2−2xy) 4x2+4y2−8=x2+y2−2xy 3x2+2xy+3y2=8