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A variable line passing through the orig...

A variable line passing through the origin intersects two given straight lines `2x + y = 4 and x + 3y = 6` at R and S respectively. A point P is taken on this variable line. Find the equation to the locus of the point P if (a) OP is the arithmetic mean of OR and OS. (b) OP is the geometric mean of OR and OS. (c) OP is an harmonic mean of OR and OS

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