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AP EAMCET2016MathematicsParabola

If (x₁, y₁ ) and (x₂, y₂ ) are the end points of a focal chord of the parabola y^2=5 x , then 4 x₁ x₂+y₁ y₂ is equal to

Options

  1. A25
  2. B5
  3. C0
  4. D5 4

Correct answer

C. 0

Step-by-step solution

Given parabola y^2=5 x Let (x₁, y₁ ) and (x₂, y₂ ) be the end points of a focal chord. So, x₁= 5 4 t₁^2 and y₁= 5 4 t₁ Since, t₁ t₂=-1 as t₁ and t₂ are the end points of a focal chord x₂= 5 4 ( 1 t₁^2 ) and y₂= 5 2 ( -1 t₁ ) Now, x₁ x₂= 25 16 and y₁ y₂=- 25 4 aligned & 4 x₁ x₂+y₁ y₂=4 ( 25 16 )- 25 4 & 25 4 - 25 4 =0 aligned

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