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

A variable line L is drawn through O(0,0) to meet the line `L_(1) " and " L_(2)` given by y-x-10 =0 and y-x-20=0 at Points A and B, respectively.
Locus of P, if `OP^(2) = OA xx OB`, is

A

`(y-x)^(2) = 100`

B

`(y+x)^(2) = 50`

C

`(y-x)^(2) = 200`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`r^(2) = (10 xx 20)/("sin" theta - "cos"theta)^(2)`
`"or " (r "sin" theta - r" cos" theta)^(2) = 200`
Hence, the locus is `(y-x)^(2) = 200`.
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