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AP EAMCET202022 Sep 2020Morning ShiftMathematicsCircleActual

If the circles x^2+y^2-2 x-2 y-7=0 and x^2+y^2+4 x+2 y+k=0 cut orthogonally, then the length of their common chord is units

Options

  1. A2
  2. B5
  3. C6 13
  4. D12 13

Correct answer

D. 12 13

Step-by-step solution

Since the given circles x^2+y^2-2 x-2 y-7=0 and x^2+y^2+4 x+2 y+k=0 cut orthogonally, then (-2)(2)+(-2)(1)=k-7 -4-2=k-7 k=1 So, equation of common chord is 6 x+4 y+8=0 3 x+2 y+4=0 Length of the chord, A B=2(A M) x^2+y^2-2 x-2 y-7=0 aligned & =2 A C^2-C M^2 & =2 9- (3+2+4)^2 9+4 & =2 117-81 13 =2 36 13 = 12 13 units aligned

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