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The length of intercept cut by the line 4 x + 4 3 y - 1 = 0 on the curve y 2 = 4 x + 3 4 is equal to

Options

  1. A4 units
  2. B9 units
  3. C12 units
  4. D16 units

Correct answer

D. 16 units

Step-by-step solution

The given line passes through the focus 1 4 , 0 , so it is a focal chord for the given parabola. Hence, its slope is tan ⁡ α = - 1 3 ∴ the length of the intercept is the same as the length of the focal chord Hence, the length of the intercept = 4 a cosec 2 α = 4 ⋅ 1 ⋅ 2 2 = 16 units

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