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NTA Abhyas JEE Main2020MathematicsParabolaPractice

O A is the chord of the parabola y 2 = 4 x (where O is the origin). A B is a chord of y 2 = 4 x and perpendicular to O A which cuts the axis of the parabola at C . If the foot of A on the axis of the parabola is D , then the length C D is equal to

Options

  1. A2 units
  2. B3 units
  3. C4 units
  4. D6 units

Correct answer

C. 4 units

Step-by-step solution

Let, A = t 2 , 2 t The slope of O A is equal to 2 t ⇒ The slope of A B is equal to - t 2 ⇒ The equation of A B is y - 2 t x - t 2 = - t 2 ⇒ C = 4 + t 2 , 0 & D = t 2 , 0 ⇒ C D = t 2 + 4 - t 2 = 4 units

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