Asymptotes of a Hyperbola

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JEE Advanced 2021

LEVELJEE Advanced

Comprehension Passage

Consider the lines

L_{1}

L_{2}

L_{1} : x 2 + y - 1 = 0

L_{2} : x 2 - y + 1 = 0

. For a fixed constant

λ

C

be the locus of a point

P

such that the product of the distance of

P

L_{1}

and the distance of

P

L_{2}

λ^{2}

y = 2 x + 1

C

R

S

, where the distance between

R

S

270

. Let the perpendicular bisector of

R S

C

at two distinct points

R^{'}

S^{'}

D

be the square of the distance between

R^{'}

S^{'}

The value of $λ^{2}$ is

The value of $D$ is