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JEE Main202120 Jul 2021Morning ShiftMathematicsParabolaActual

Let the tangent to the parabola S : y 2 = 2 x at the point P 2 , 2 meet the x - axis at Q and normal at it meet the parabola S at the point R . Then the area (in sq. units) of the triangle P Q R is equal to:

Options

  1. A25 2
  2. B35 2
  3. C15 2
  4. D25

Correct answer

A. 25 2

Step-by-step solution

We have, y 2 = 2 x Tangent at P 2 , 2 is y 2 = 2 1 2 x + 2 ⇒   2 y = x + 2 It meets x - axis at y = 0 i.e., x = - 2 ∴     Q ≡ - 2 , 0 Normal at P is ⇒     y - 2 = - 2 x - 2 ⇒     y = 6 - 2 x ∴ Solving with y 2 = 2 x , we get 6 - 2 x 2 = 2 x ⇒     4 x 2 + 36 - 24 x = 2 x ⇒     4 x 2 - 26 x + 36 = 0 ⇒     2 x 2 - 13 x + 18 = 0 ⇒     x = 13 ± 169 - 144 4 = 13 ± 5 4 ⇒ &#

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