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NTA Abhyas JEE Main2020MathematicsParabolaPractice

The length of the chord y = 3 x - 2 3 intercepted by the parabola y 2 = 4 x - 1 is equal to

Options

  1. A4 3 units
  2. B8 3 units
  3. C16 3 units
  4. D4 3 units

Correct answer

C. 16 3 units

Step-by-step solution

Focus of y 2 = 4 x - 1 is 2,0 which satisfies the equation y = 3 x - 2 3 . Hence, line y = 3 x - 2 3 is a focal chord. Now, the length of the focal chord equals to 4 a c o s e c 2 θ where a = 1 and tan ⁡ θ = 3   o r   θ = 6 0 o ⇒ length of chord = 4 × c o s e c 2 60 o = 4 × 4 3 = 16 3 units

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