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Let P Q be the focal chord of the parabola y 2 = 4 x. If the centre of the circle having P Q as its diameter lies on the line y = - 4 5 , then the length (in units) of chord P Q is

Correct answer

7.2

Step-by-step solution

Let P is t 2 , 2 t then Q is 1 t 2 , - 2 t mid point of P Q is t 2 + 1 t 2 2 , 2 t - 2 t 2 ⇒ t - 1 t = - 4 5 ⇒ t 2 + 1 t 2 - 2 = 16 5 ⇒ t 2 + 1 t 2 + 2 = 36 5 ⇒ t 2 + 1 + 1 t 2 + 1 = 7.2 P S + S Q = 7.2 ⇒ P Q = 7.2 P S = a + a t 2 , P Q = a + a t 2 where a = 1

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