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A variable line L drawn through O(0,0) t...

A variable line L drawn through O(0,0) to meet line l1: y-x-10=0 and L2:y-x-20=0 at the point A and B respectively then locus of point p is ' such that `(OP)^(2) = OA . OB, `

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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