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NTA Abhyas JEE Main2020MathematicsParabolaPractice

Let the focus S of the parabola y 2 = 8 x lie on the focal chord P Q of the same parabola. If the length Q S = 3 units, then the ratio of length P Q to the length of the latus rectum of the parabola is

Options

  1. A2 5
  2. B4 5
  3. C5 4
  4. D9 8

Correct answer

D. 9 8

Step-by-step solution

For the focal chord P Q , we know that, P S , 4 , S Q are in H.P. ⇒ 1 P S , 1 4 , 1 3 are in A.P. ⇒ 1 P S = 2 4 - 1 3 = 1 6 ⇒ P S = 6 ⇒ P Q = 6 + 3 = 9 ⇒ P Q length of l a t u s re c t u m = 9 8

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