JEE Main2018MathematicsParabolaActual

If the tangent at 1 , 7 to the curve x 2 = y - 6 touch the circle x 2 + y 2 + 16 x + 12 y + c = 0 then the value of c is:

Options

A95
B195
C185
D85

Correct answer

A. 95

Step-by-step solution

Differentiating x 2 = y - 6 with respect to x , 2 x = d y d x d y d x 1,7 = 2 × 1 = 2 Hence, equation of tangent is y - 7 = 2 ( x - 1 ) ⇒ y = 2 x + 5 Distance from centre = - 6 - 2 - 8 - 5 1 2 + 2 2 ⇒ 5 5 = 5 Radius of circle =   8 2 + 6 2 - c ⇒ 100 - c =   5 ⇒ c = 95

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