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JEE Main202226 Jun 2022Morning ShiftMathematicsParabolaActual

Let the normal at the point P on the parabola y 2 = 6 x pass through the point 5 , - 8 . If the tangent at P to the parabola intersects its directrix at the point Q , then the ordinate of the point Q is

Options

  1. A- 9 4
  2. B9 4
  3. C- 5 2
  4. D- 3

Correct answer

A. - 9 4

Step-by-step solution

Given y 2 = 6 x comparing with y 2 = 4 a → a = 3 2 Now normal at P is given by P 3 2 t 2 , 3 t y + t x = 3 t + 3 2 t 3 Now this normal is passing through 5 , - 8 So - 8 + 5 t = 3 t + 3 2 t 3 ⇒ - 16 + 10 t = 6 t + 3 t 3 ⇒ 3 t 3 - 4 t + 16 = 0 Now solving above equation we get t = - 2 So tangent at P is given by t y = x + a t 2 putting a & t we get - 2 y = x + 3 2 × 4 - 2 y = x + 6 Now tangent is intersecting at directrix which is x = - 3 2 So - 2 y = - 3 2 + 6 ⇒ y = 3 4 - 3 = - 9 4 So po

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