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If A F B is a focal chord of the parabola y 2 = 4 a x such that A F = 4 and F B = 5 , then the latus-rectum of the parabola is equal to

Options

  1. A80
  2. B9 80
  3. C9
  4. D80 9

Correct answer

D. 80 9

Step-by-step solution

Given: F A = 4 and F B = 5 , where F A and F B are segments of focal chord. Since, we know that harmonic mean of F A ,   F B is equal to semi latus rectum. Therefore, 2 2 a = 1 A F + 1 F B ⇒ a = 20 9 ⇒ 4 a = 80 9

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