If the line x-2y=m (m Z) intersects the circle x^2+y^2=2x+4y at two distinct points, then the number of possible values of m are

MHT CET 2023 Mathematics question

If the line () intersects the circle at two distinct points, then the number of possible values of m are

(A)8
(B)9Correct
(C)10
(D)11

Answer: (B)

Solution

Write the circle as : centre , radius . The line cuts the circle at two distinct points iff the distance of the centre from the line is less than the radius:

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Question ID VK-098362