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NTA Abhyas JEE Main2020MathematicsParabolaPractice

If three normals are drawn from the point c , 0 to the parabola y 2 = 4 x and two of which are perpendicular, then the value of c is equal to

Options

  1. A3
  2. B4
  3. C5
  4. D6

Correct answer

A. 3

Step-by-step solution

Equation of the normal in slope form is y = m x - 2 m - m 3 which passes through c , 0 ⇒ 0 = m c - 2 m - m 3 ⇒ m 3 + 2 - c m = 0 ⇒ m = 0 or m 2 + 2 - c = 0 ⇒ m 1 m 2 = 2 - c 1 = - 1 ⇒ c = 3

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