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JEE Main202310 Apr 2023Morning ShiftMathematicsParabolaActual

Let a common tangent to the curves y 2 = 4 x and x - 4 2 + y 2 = 16 touch the curves at the points P and Q . Then P Q 2 is equal to ________.

Correct answer

0

Step-by-step solution

Given, Common tangent to the curves y 2 = 4 x and x - 4 2 + y 2 = 16 touch the curves at the points P and Q Let, the equation of tangent be, y = m x + a m , where a = 1 is focus and m is slope, So, equation of tangent to parabola will be, y = m x + 1 m Also line is tangent to circle, So, using perpendicular distance formula from centre 4 ,   0 to tangent which will be radius r = 4 , we get, 4 m + 1 m m 2 + 1 = 4 ⇒ 16 m 2 + 1 m 2 + 8 = 16 m 2 + 16 ⇒ m 2 = 1 8 ⇒ m = ± 1 2 2 Now if m = 1 2

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