Comprehension
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 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 \(\sqrt{270}.\)
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’.
\(L_1: x\sqrt{2} + y - 1 = 0\)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 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 \(\sqrt{270}.\)
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’.
Question: 1
The value of λ2 is _______ ?
The value of λ2 is _______ ?
Updated On: Apr 24, 2024
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Correct Answer: 9
Solution and Explanation
The value of λ2 is 9.
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Question: 2
The value of 𝐷 is ___ .
The value of 𝐷 is ___ .
Updated On: Apr 24, 2024
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Correct Answer: 77.14
Solution and Explanation
The value of 𝐷 is 77.14.
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