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JEE Main202228 Jul 2022Morning ShiftMathematicsParabolaActual

If the tangents drawn at the points P and Q on the parabola y 2 = 2 x - 3 intersect at the point R 0 , 1 , then the orthocentre of the triangle P Q R is

Options

  1. A0 , 1
  2. B2 , - 1
  3. C6 , 3
  4. D2 , 1

Correct answer

B. 2 , - 1

Step-by-step solution

On plotting the diagram of given value we get, Now given parabola is y 2 = 2 x - 3 ⇒ y 2 = 2 x - 3 2 Let a point on parabola be P = 3 2 + t 2 2 , t Equation of tangent at P will be y t = x + 3 2 + t 2 2 - 3 ∵     R 0 , 1 lies on this tangent Then t = t 2 2 - 3 2 i.e. t = 3 or - 1 . So P ≡ 6 , 3   &   Q ≡ 2 , - 1 Now triangle P Q R is right angled at Q , so 2 , - 1 is the orthocentre of the triangle.

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