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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) = 50` b. `(y-x)^(2) = 200` c. `(y-x)^(2) = 100` d. none of these

A

`(y-x)^(2) = 80`

B

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

C

`(y-x)^(2) = 64`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(1)/(r^(2)) = ("sin" theta - "cos" theta)^(2)/(100) + ("sin" theta -"cos" theta)^(2)/(400)`
`"or " 400 = 5(r "sin" theta - r "cos" theta)^(2)`
Hence, the locus is `400=5(x-y)^(2), i.e., (x-y)^(2)= 80.`
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