Question

Chookng oA as x axus
( A=(2,0) )
( B=(0, gamma) )
and any pomt Pon he qe
in ( (2 cos theta, 8 sin theta) )
( operatorname{sf}(x, y) )
is the centerid of ( triangle P^{circ} A B ), then ( 3 x=r cos theta+r+0 )
and ( 3 y=r sin theta+0+gamma )
( (3 x-8)^{2}+(3 y-gamma)^{2}=gamma^{2} )
Kence, Louns of
Pis a ciccle

# 3. Let AB be a chord of the circle + y = r subtending a right angle at the centre. Thenthe locus of the centroid of the APAB as P moves on the circle, is (2001, 1M) (a) a parabola (b) a circle c) an ellipse (d) a pair of straight lines

Solution