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AP EAMCET202124 Aug 2021Morning ShiftMathematicsCircleActual

If the circles x^2+y^2-6 x-8 y-12=0 and x^2+y^2-4 x+6 y+k=0 are perpendicular to each other, then ' k ' equals

Options

  1. A4
  2. B0
  3. C-2
  4. D12

Correct answer

B. 0

Step-by-step solution

aligned & C₁: x^2+y^2-6 x-8 y-12=0 & C₂: x^2+y^2-4 x+6 y+k=0 aligned Both the circles are perpendicular to each other. aligned g₁ & =-3, f₁=-4, c₁=-12 & g₂=-2, f₂=3, c₂=k aligned If two circles cuts perpendicularly to each other. array rlrl & 2 g₁ g₂+2 f₁ f₂ & =c₁+c₂ & 2(-3)(-2)+2(-4)(3) & =-12+k & 12+(-24) & =-12+k & & -12 & =-12+k & k & =0 array

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