Circle 1 Question 8

8. Let AB be a chord of the circle x2+y2=r2 subtending a right angle at the centre. Then, the locus of the centroid of the PAB as P moves on the circle, is

(2001,1 M)

(a) a parabola

(b) a circle

(c) an ellipse

(d) a pair of straight lines

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Answer:

Correct Answer: 8. (a)

Solution:

  1. Choosing OA as X-axis, A=(r,0),B=(0,r) and any point P on the circle is (rcosθ,rsinθ). If (x,y) is the centroid of PAB, then

 and 3y=rsinθ+0+r(3xr)2+(3yr)2=r2

Hence, locus of P is a circle.



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