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

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a 2 + b 2 ​ = ( 6 k ) a 2 + b 2 = ( 6 k ) 2 Let ( h , k ) is centroid h = 3 a + 0 + 0 ​ k = 3 0 + b + 0 ​ a = 3 h b = 3 k ( 3 h ) 2 + ( 3 k ) 2 = ( 6 k ) 2 x 2 + y 2 = ( 2 k ) 2

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