Question

Consider the lines L1 and L2 defined by
$L_1: x\sqrt{2} + y - 1 = 0$and $L_2: x\sqrt{2} - y + 1 = 0$
For a fixed constant λ, let C be the locus of a point P such that the product of the distance of P from L1 and the distance of P from L2 is λ2. 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’.