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AP EAMCET2015MathematicsCircle

The sum of the minimum and maximum distance of the point (4,-3) to the circle x^2+y^2+4 x-10 y-7=0 , is

Options

  1. A10
  2. B12
  3. C16
  4. D20

Correct answer

D. 20

Step-by-step solution

Let the given point be P(4,-3) and the given circle is x^2+y^2+4 x-10 y-7=0 Centre of circle = C (-2,5) Radius = (-2)^2+(5)^2+7 = 4+25+7 = 36 =6 Maximum distance, a=C P+r Minimum distance, b=C P-r Sum of the maximum and minimum distance, a+b=C P+r+C P-r=2 C P and C P= (-2-4)^2+(5+3)^2 = 36+64 = 100 =10 Thus, a+b=2 C P=2 10=20

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