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NTA Abhyas JEE Main2020MathematicsParabolaPractice

Let the focus S of the parabola y 2 =8 x lies on the focal chord P Q of the same parabola. If P S = 6 , then the square of the slope of the chord P Q is

Options

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

Correct answer

B. 4 5

Step-by-step solution

We know that, P S ,   4 ,   S Q are in H . P . ⇒ 1 6 , 1 4 , 1 S Q are in A . P . ⇒ 1 S Q = 2 4 - 1 6 = 1 3 ⇒ S Q = 3 ⇒ P Q = 6 + 3 = 9 = 4 c o s e c 2 θ (where, tan ⁡ θ is the slope of P Q ) ⇒ 1 + cot 2 ⁡ θ = 9 4 ⇒ cot 2 ⁡ θ = 5 4 ⇒ tan 2 ⁡ θ = 4 5

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