The tangent to the curve y=x^2+6 at (1,7) touches the circle x^2+y^2+16x+12y+c=0 at the point

JEE Advanced Mathematics question

The tangent to the curve at touches the circle at the point

(A)
(B)
(C)
(D)Correct

Answer: (D)

Solution

at , so the tangent is , i.e. … (1). The circle's centre is . The point of contact is the foot of the perpendicular from to (1). The perpendicular through has

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Question ID VK-110178