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JEE Main20265 April 2026Evening ShiftMathematicsParabolaActual

Let the directrix of the parabola P: y^2 = 8x , cut x -axis at the point A . Let B( , ) , > 1 , be a point on P such that the slope of AB is 3/5 . If BC is a focal chord of P , then six times the area of ABC is :

Options

  1. A80
  2. B160
  3. C174
  4. D192

Correct answer

B. 160

Step-by-step solution

For the parabola P: y^2 = 8x , we have 4a = 8 a = 2 . The equation of the directrix is x = -a x = -2 . Since the directrix cuts the x -axis at A , the coordinates of A are (-2, 0) . Let the coordinates of point B on the parabola be (2t₁^2, 4t₁) . The slope of AB is given as 3 5 . 4t₁ - 0 2t₁^2 - (-2) = 3 5 2t₁ t₁^2 + 1 = 3 5 10t₁ = 3t₁^2 + 3 3t₁^2 - 10t₁ + 3 = 0 (3t₁ - 1)(t₁ - 3) = 0 t₁ = 1 3 or t₁ = 3 . For t₁ = 1 3 , = 2 ( 1 3 )^2 = 2 9 , which is rejected since > 1 . For t₁ = 3 , = 2(3)^2 = 18 > 1 . Thus, B is (

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