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NTA Abhyas JEE Main2020MathematicsParabolaPractice

The points A 3 , 6 and B lie on the parabola y 2 = 4 a x , such that the chord A B subtends 90 ° at the origin, then the length of the chord A B is equal to

Options

  1. A15 13 units
  2. B12 17 units
  3. C9 17 units
  4. D9 10 units

Correct answer

A. 15 13 units

Step-by-step solution

Since the chord subtends a right angle at the origin, ∴ t 1 t 2 = - 4 Now, the point A lies on the parabola, ∴ 36 = 4 a 3 ⇒ a = 3 i.e. A 3 , 6 = 3 t 1 2 , 6 t 1 ⇒ t 1 = 1 ⇒ t 2 = - 4 So, B ≡ 48 , - 24 Hence, the length of the chord A B = 15 13 units

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