CircleHard

Question

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

Options

A.x2 + y2 = (2k)2
B.x2 + y2 = (3k)2
C.x2 + y2 = (4k)2
D.x2 + y2 = (6k)2

Solution

    
Let centroid of the triangle
OAB be (α, β)
∴    a = 3α, b = 3β
a2 + b2 = 36k2
⇒ 9α2 + 9β2 = 36k2
Locus of (α, β) is
x2 + y2 = 4k2

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