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Consider the lines L1 and L2 defined by ...

Consider the lines `L_1 and L_2` defined by
`L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0`
For a fixed constant `lambda`, let C be the locus of a point P such that the product of the distance of P from `L_1` and the distance of P from `L_2` is `lambda^2`. The line `y=2x+1` meets C at two points R and S, where the distance between R and S is `sqrt(270)`.
Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'.
The value of `D` is

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Consider the lines L_1 and L_2 defined by L_1:xsqrt2+y-1=0 and L_2:xsqrt2-y+1=0 For a fixed constant lambda , let C be the locus of a point P such that the product of the distance of P from L_1 and the distance of P from L_2 is lambda^2 . The line y=2x+1 meets C at two points R and S, where the distance between R and S is sqrt(270) . Let the perpendicular bisector of RS meet C at two distinct points R' and S' . Let D be the square of the distance between R' and S'. The value of lambda^2 is

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