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JEE Main202120 Jul 2021Morning ShiftMathematicsParabolaActual

Let y = m x + c , m > 0 be the focal chord of y 2 = - 64 x , which is tangent to ( x + 10 ) 2 + y 2 = 4 . Then, the value of 4 2 ( m + c ) is equal to______

Correct answer

0

Step-by-step solution

We have, y 2 = - 64 x Coordinates of focus of parabola is : - 16 , 0 y = m x + c is focal chord, hence ⇒ c = 16 m     . . . 1 y = m x + c is tangent to ( x + 10 ) 2 + y 2 = 4 , therefore y = m x + 10 ± 2 1 + m 2 ⇒ c = 10   m ± 2 1 + m 2 ⇒ 16   m = 10   m ± 2 1 + m 2 ⇒ 6 m = 2 1 + m 2 ,     m > 0 ⇒ 9   m 2 = 1 + m 2 ⇒ m = 1 2 2   &   c = 8 2 Then, 4 2 m + c = 4 2 17 2 2 = 34

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