Equation of given circle is x‌2 + y‌2 = 4 Its centre, 0 = (0,0) and radius, r = 2 Draw OM ⊥ AB Clearly M is the mid-point of AB which subtends a right angle at O. In ΔAOB, OA = OB radius ∴ ∠A = ∠B =
Ï€
4
and in ΔOMA, sinA =
OM
OA
sin
Ï€
4
=
OM
2
⇒
1
√2
=
OM
2
⇒ OM=√2 ...(1) Let M = (x, y) then OM = √x2+y2 ...(2) From (1) and (2), x2+y2 = 2 This is the required equation of locus.