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MHT CET202526 Apr 2025Morning ShiftMathematicsCircleActual

The least distance of the point A(10,7) from the circle x^2+ y ^2-4 x-2 y -20=0 is length of seg. AM . If MM ^ is the diameter of the circle, then the lengths of AM and AM ^ are respectively _______ , ______ units

Options

  1. A5,10
  2. B4,15
  3. C5,15
  4. D2,10

Correct answer

C. 5,15

Step-by-step solution

The given circle x^2 + y^2 - 4x - 2y - 20 = 0 has center (2, 1) and radius 5 units. For point A(10, 7) , the distance from the center is AC = (10-2)^2 + (7-1)^2 = 10 units. Since AC > r , point A lies outside the circle. The least distance from the circle is AC - r = 10 - 5 = 5 units. The greatest distance from the circle is AC + r = 10 + 5 = 15 units. Answer: C

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