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JEE Main202225 Jul 2022Evening ShiftMathematicsParabolaActual

The tangents at the points A 1 , 3 and B 1 , - 1 on the parabola y 2 - 2 x - 2 y = 1 meet at the point P . Then the area (in unit 2 ) of the triangle P A B is:

Options

  1. A4
  2. B6
  3. C7
  4. D8

Correct answer

D. 8

Step-by-step solution

Given, y 2 - 2 x - 2 y = 1 ⇒ y - 1 2 = 2 x + 1 Tangents are drawn at 1 , 3 & 1 , - 1 , on plotting the diagram we get, ​​​​​​​ Now, tangent as A : 2 y - x - 5 = 0 using T = 0 Intersection with y = 1 is x = - 3 Hence, point P is - 3 , 1 We can see diagram has symmetry So, area of ∆ P A B = 2 × 1 2 × 1 - - 3 × 3 - 1 = 8 sq . units

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