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Q.

A variable line passing through fixed point (a, b) intersect the coordinate axes at A and B if O is origin then the locus of centroid of the OAB is

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a

bx+ay−2xy=0

b

ax+by−3xy=0

c

ax+by−2xy=0

d

bx+ay−3xy=0

answer is A.

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Detailed Solution

Equation of AB 

y−bx=(x−a)m

Let (h, k) be centroid of ΔOAB

h=a−bm3, k=b−am3

∴  Locus of the (h, k) is  ⇒(3x−a−b)(3y−b−a)=1⇒bx+ay−3xy=0

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