JEE Advanced 2021 · Paper 1, Mathematics question 10

Question Stem for Question Nos. 9 and 10

Consider the lines $L_1$ and $L_2$ defined by
$$L_1:\ x\sqrt2 + y - 1 = 0 \quad\text{and}\quad L_2:\ x\sqrt2 - y + 1 = 0$$
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 $S'$.