Question Stem
Consider the lines $$L_1$$ and $$L_2$$ defined by
$$L_1 : x \sqrt{2} + y - 1 = 0$$ and $$L_2 : x \sqrt{2} - y + 1 = 0$$
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 $$S′$$.