1.

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

Answer»

`(y-x)^(2) = 100`
`(y+x)^(2) = 50`
`(y-x)^(2) = 200`
NONE of these

Solution :`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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