A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant then the line passes through-

Options

A. A fixed piont
B. A variable point
C. Origin
D. None of these

Answer

A

Explanation

Let line is `(x)/(a) +(y)/(b) =1` and `(1)/(a) +(1)/(b) =lambda rArr (1)/(lambdaa)+(1)/(lambdab) =1`
`(x)/(a) +(y)/(b) =(1)/(lambdaa) +(1)/(lambdab)`
`(1)/(a)(x-(1)/(lambda))+(1)/(b)(y-(1)/(lambda))=0`
Lines always passes through `((1)/(lambda),(1)/(lambda))`