A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R isA. `9x +6y = 20`B. `6x - 9y = 20`C. `6x +9y = 20`D. none of these

A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y =

1.	A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R isA. `9x +6y = 20`B. `6x - 9y = 20`C. `6x +9y = 20`D. none of these
Answer» Correct Answer - C Let the line L be `(x)/(cos theta) =(y)/(sin theta)` Then `OP = (5)/(2cos theta +3 sin theta)` and `OQ = (10)/(2cos theta +3 sin theta)` and let `OR = r` Then according to condition `20 = 6r cos theta +9r sin theta` `:.` locus is `6x +9y = 20`

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