BITSAT 2019 Paper

(c)

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 =

π

4

and in ΔOMA, sinA =

OM

OA

sin

π

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.