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JEE Main202116 Mar 2021Morning ShiftMathematicsParabolaActual

If the three normals drawn to the parabola, y 2 = 2 x pass through the point a , 0 , a ≠ 0 , then a must be greater than :

Options

  1. A1 2
  2. B- 1 2
  3. C- 1
  4. D1

Correct answer

D. 1

Step-by-step solution

Let the equation of the normal be y = m x - 2 a m - a m 3 Here 4 a = 2 a = 1 2 y = m x - m - 1 2 m 3 It passes through A ( a ,   0 ) then 0 = a m - m - 1 2 m 3 m = 0 , m 2 - 2 ( a - 1 ) = 0 For real values of m 2 ( a - 1 ) > 0 ⇒ a > 1

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