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Straight Lines and Pair of Straight Lines question

2021 · Shift 1 · Q28

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JEE Advanced
Mathematics
Straight Lines and Pair of Straight Lines
2021 · Shift 1 · Q28

Straight Lines and Pair of Straight Lines question

2021 · Shift 1 · Q28

JEE AdvancedMathematicsStraight Lines and Pair of Straight LinesNumerical+2 / −1

Consider the lines L1 and L2 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 L1 and the distance of P from L2 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'. The value of

\lambda

2 is

\underline{\hspace{2cm}}

.

Numerical answer

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