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A variable line L is drawn through O (0,...

A variable line L is drawn through O (0,0) to meet the lines L 1 ​ :y−x−10=0 and L 2 ​ :y−x−20=0 at the points A and B respectively. A point P is taken on L such that OP 2 ​ = OA 1 ​ + OB 1 ​ and P,A,B lies on same side of origin O. The locus of P is

A

`9x +6y = 20`

B

`6x - 9y = 20`

C

`6x +9y = 20`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
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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