A variable straight line passes through ...

A variable straight line passes through a fixed point `(a, b)` intersecting the co-ordinates axes at A & B. If 'O' is the origin, then the locus of the centroid of the triangle `OAB` is (A) `bx+ ay-3xy=0` (B) `bx+ay-2xy=0` (C) `ax+by-3xy=0` (D) `ax+by-2xy=0`.

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