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AP EAMCET202119 Aug 2021Morning ShiftMathematicsCircleActual

The point which has the same power with respect to each of the circles x 2 + y 2 - 8 x + 40 = 0 , x 2 + y 2 - 5 x + 16 = 0 and x 2 + y 2 - 8 x + 16 y + 160 = 0 is

Options

  1. A− 8 , − 15 2
  2. B8 , − 15 2
  3. C8 , 15 2
  4. D− 8 , 15 2

Correct answer

B. 8 , − 15 2

Step-by-step solution

Given circle equations x 2 + y 2 - 8 x + 40 = 0 - - - ( I ) x 2 + y 2 - 5 x + 16 = 0 - - - - ( I I ) x 2 + y 2 - 8 x + 16 y + 160 = 0 - - - - I I I Power of point with respect to circle = S 1 For point P 8 ,   - 15 2 With respect to equation I = 64 + 225 4 - 64 + 40 = 385 4 With respect to equation I I =   64 + 225 4 - 40 + 16 = 385 4 With respect to third circle = 385 4 The remaining points in other options are not having same power. So required point is 8 ,   - 15 2 .

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