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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let P ≡ a , 0 ,   Q ≡ - 1 , 0 and R ≡ 2 , 0 are three given points. If the locus of the point S satisfying the relation S Q 2 + S R 2 = 2 S P 2 is 2 x + 3 = 0 , then the sum of all possible values of a is

Options

  1. A1
  2. B- 4
  3. C3
  4. D- 3

Correct answer

D. - 3

Step-by-step solution

We have, P ≡ a , 0 , Q ≡ - 1 , 0 , R ≡ 2 , 0 . Let, S ≡ x , y Now, given that S Q 2 + S R 2 = 2 S P 2 . Hence, x + 1 2 + y 2 + x - 2 2 + y 2 = 2 x - a 2 + y 2 or 2 x 2 + 2 y 2 - 2 x + 5 = 2 x 2 + 2 y 2 - 4 a x + 2 a 2 or 4 a - 2 x = 2 a 2 - 5 or 2 x + 3 = 0 or x = - 3 2 = 2 a 2 - 5 4 a - 2 ⇒ a = 1 , - 4

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