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Let `AB` be a chord of the circle `x^2+y^2=r^2` subtending a right angle at the center. Then the locus of the centroid of the `Delta PAB` as `P` moves on the circle is(1) A parabola(2) A circle(3) An ellipse(4) A pair of straight lines |
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Answer» `A{rcos(theta+90^0),rsin(theta+90^0)}` `=A(-rsintheta,rcostheta)` `theta=0` `B(r,0),A(0,r)` Contract of`/_PAB is (alpha,beta)` `alpha=(r+0+rcostheta)/3=3alpha-r=rcostheta-(1)` `beta=(0+r+rsintheta)/3=3beta-r=rsintheta-(2)``(3alpha-r)^2+(3beta-r)^2=r^2cos^2theta+r^2sin^2theta=r^2` `(alpha-r/3)^2+(beta-r/3)^2=(r/3)^2` `(r/3,r/3),(r/3)` option b is correct. |
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