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Tangents to the parabola y 2 = 4 a x at P a t 1 2 , 2 a t 1 and Q a t 2 2 , 2 a t 2 meet at T . If △ P T Q is right-angled at T , then 1 P S + 1 Q S is equal to (where, S is the focus of the given parabola)

Options

  1. A1 a
  2. B2 a
  3. C1 2 a
  4. D1 4 a

Correct answer

A. 1 a

Step-by-step solution

T lies on the directrix and P Q is the focal chord. ⇒ t 1 t 2 = - 1 1 P S = 1 a 1 + t 1 2 , 1 Q S = 1 a 1 + t 2 2 = t 1 2 a 1 + t 1 2 So, 1 P S + 1 Q S = 1 a

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