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KCET2012MathematicsCircle

The least and the greatest distances of the point (10,7) from the circle x²+y²-4 x-2 y-20=0 are

Options

  1. A10,5
  2. B15,20
  3. C12,16
  4. D5,15

Correct answer

D. 5,15

Step-by-step solution

Given, x²+y²-4 x-2 y-20=0 Here, g=-2, f=-1, c=-20 Centre =(-g,-f)=(2,1) Radius aligned &= g²+f²-c = (-2)²+(-1)²-(-20) &= 4+1+20 &= 25 =5 aligned i.e., The distance between the points (2,1) and aligned (10,7) &= (10-2)²+(7-1)² &= 64+36 &= 100 =10 units aligned The least distance of the point (10,7) from the circle =10-5=5 units and the greatest distance of the point (10,7) from the circle =10+5=15 units.

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