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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

If the image of the point M λ , λ 2 on the line x + y = λ 2 is N 0,2 , then the sum of the square of all the possible values of λ is equal to

Options

  1. A5
  2. B2
  3. C1
  4. D4

Correct answer

A. 5

Step-by-step solution

Since the mid-point of the line segment M N lie on the given line, ⇒ λ 2 + λ 2 + 2 2 = λ 2 … . . i Also, the line segment M N is perpendicular to the given line ⇒ λ 2 - 2 λ - 0 × - 1 = - 1 … . . i i As i and i i must be satisfied simultaneously, ∴ On solving, we get, λ = - 1,2 ⇒ λ 1 2 + λ 2 2 = 1 + 4 = 5

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