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AP EAMCET202423 May 2024Morning ShiftMathematicsCircleActual

If the circles x^2+y^2+2 x+2 y-8=0 and x^2+y^2-2 x+ y-14=0 intersect orthogonally, then the distance between their centres is

Options

  1. A242
  2. B970
  3. C629
  4. D541

Correct answer

C. 629

Step-by-step solution

S₁ x^2+y^2+2 x+2 y-8=0 aligned & (g₁, f₁, c₁ )=( , 1,-8) & S₂ x^2+y^2-2 x+ y-14=0 & (g₂, f₂, c₂ )= (-1, 2 ,-14 ) aligned S₁ and S₂ cuts orthogonally 2 g₁ g₂+2 f₁ f₂=c₁+c₂ -2 + =-8-14 =22 Centre of S₁ (C₁ )=(-22,-1) Centre of S₂ (C₂ )=(1,-11)C₁ C₂= (23)^2+(10)^2 = 629 .

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