Question

The locus of the middle points of the chords of the circle x2 + y2 = 4a2, which subtends a right angle at the centre of the circle is-

• A. x + y = 2a
• B. x2 + y2 = 2a2
• C. x2 + y2 = a2
• D. x2 + y2 = a22

Answer 1

Answer: (B)

x2 + y2 = 2a2

Answer 2

Since ŠAOB = 90⁰

PA = PB = PO = AO cos 45ŗ = $\frac{2a}{\sqrt{2}}$ = a $\sqrt{2}$

Since OP = a$\sqrt{2}$, locus of P is the

circle with O as centre and radius a$\sqrt{2}$

and its equation is x2 + y2 = 2a2.