Consider the lines L1 and L2 defined byL1:x√2+y−1=0 and L2:x√2−y+1=0For 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 √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

Consider the lines L1 and L2 defined byL1:x√2+y−1=0 and L2:x√2�

1.	Consider the lines L1 and L2 defined byL1:x√2+y−1=0 and L2:x√2−y+1=0For 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 √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
Answer» 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 $λ,$ 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 $λ^{2}$ . The line $y = 2 x + 1$ meets $C$ at two points $R$ and $S,$ where the distance between $R$ and $S$ is $\sqrt{270} .$ Let the perpendicular bisector of $R S$ 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