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

Correct answer

3.6

Step-by-step solution

Let, P is t 2 , 2 t then, Q is 1 t 2 , - 2 t Midpoint 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 If S is the focus, then P S + S Q = 7.2 ⇒ P Q = 7.2 Hence, radius = 3.6 units

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