JEE Main | 2018CircleHard

Question

If the tangent at (1, 7) to the curve x2 = y - 6 touches the circle x2 + y2 + 16x + 12y + c = 0 then the value of c is :

Options

A.

185

B.

85

C.

95

D.

195

Solution


Equation of tangent at (1, 7) to x2 = y - 6 is
2x - y + 5 = 0.
Now, perpendicular from centre O(-8, -6) to 2x - y + 5 = 0 should be equal to radius of the circle
-16+6+55=64+36-C
5=100-C
then, C = 95

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