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MHT CET202314 May 2023Morning ShiftMathematicsCircleActual

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

Options

  1. A8
  2. B9
  3. C10
  4. D11

Correct answer

B. 9

Step-by-step solution

Centre of circle is (1,2) and radius = 1+4-0 = 5 Since the line intersects the circle at two points, length of perpendicular from the centre < radius aligned & | 1-2(2)-m 1+4 | < 5 & | m +3| < 5 & -5 < m +3 < 5 & -8 < m < 2 aligned The number of possible values of m =9

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