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Manipal MET2013MathematicsParabola

An equlateral triangle S A B is inscribed in the parabola y^2=4 a x having its focus at S . If chord A B lies towards the lefit of S , then side length of this triangle is

Options

  1. A2 a(2- 3 )
  2. B4 a(2- 3 )
  3. Ca(2- 3 )
  4. D8 a(2- 3 )

Correct answer

B. 4 a(2- 3 )

Step-by-step solution

Let A (a t₁^2, 2 a t₂ ), B (a t₂^2,-2 a t₂ ) We have, m_ A S = ( 5 6 ) 2 a t₁ a t₁^2-a =- 1 3 t₁^2+2 3 t₁-1=0 t₁=- 3 2 Clearly, t₁=- 3 -2 is rejected. thus, t₁=(2- 3 ) , Hence, A B=4 a t₁=4 a(2- 3 ) .

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