Locus of the mid-points of the chords of the circle x2+y2=4 which subtend a right angle at the centre is
Let AB = a
⟹AC=CB=a2
Given that ∠AOB=90∘
⟹AB2=OA2+OB2
a2=r2+r2=2r2=2×4=8
AB is any chord and C(x1,y1) be the midpoint of AB
In △OAC
OC⊥AC
⟹OC2=OA2–AC2
x21+y21=r2−a24
x21+y21=r2−2r24=r22=42=2