Let four points A(x1,y1),B(x2,y2),C(x3,y3) and D(x4,y4) ∴OA2=x12+y12 OB2=x22+y22 OC2=x32+y32 and OD2=x42+y42 Such that OA2+OB2+OC2+OD2 =Σx12+Σy12=4a2 From Eq. (ii) x=
b2
y
From Eq. (i) (
b2
y
)
y
2
+y2=a2 ⇒b4+y4=a2y2⇒y4−a2y2+b4=0 This is an equation of 4 th degree in y and its four roots are y1,y2,y3,y4, then y1y2y3y4=b4