Q.

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at A and B, then the locus of the centroid of triangle OAB is

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a

x2+y2=(2k)2

b

x2+y2=(3k)2

c

x2+y2=(4k)2

d

x2+y2=(6k)2

answer is A.

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Detailed Solution

Let the centroid of triangle OAB be (p, q).Hence, points A and B are (3p,0) and (0,3q), respectively.But diameter of circle, AB = 6kHence, 9p2+9q2=6kTherefore, the locus of (p, q) is x2+y2=4k2.
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If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at A and B, then the locus of the centroid of triangle OAB is