JEE Advanced 2021 Paper 1

Paragraph for next 2 questions 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'.