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

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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

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