A line parallel to the line x-3y=2 touches the circle x^2+y^2-4x+2y-5=0 at the point

JEE Advanced Mathematics question

A line parallel to the line touches the circle at the point

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

Answer: (B),(C)

Solution

Centre , radius . The point of contact of a tangent parallel to lies on the radius perpendicular to it, i.e. along the normal direction , whose length is , exactly the radius. So the points of contact are

C±(1,-3)=(3,-4)\ and\ (1,2).

Check: tangent at

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Question ID VK-108980