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AP EAMCET202021 Sep 2020Evening ShiftMathematicsCircleActual

The radical axis of any two circles is to the line joining their centres

Options

  1. AParallel
  2. BPerpendicular
  3. CIntersecting but not perpendicular
  4. DCan't be determined

Correct answer

B. Perpendicular

Step-by-step solution

The radical axis of any two circles is perpendicular to the line joining their centres. Let, the equation of two circles are ( aligned x^2+y^2+2 g₁ x+2 f₁ y+c₁ & =0 x^2+y^2+2 g₂ x+2 f₂ y+c₂ & =0 aligned ) and (x^2+y^2+2 g₂ x+2 f₂ y+c₂=0 ) The equation of the radical axis is (2 (g₁-g₂ ) x+2 (f₁-f₂ ) y+ (c₁-c₂ )=0 ) ...(i) ( ) Slope of line (i) is (- g₁-g₂ f₁-f₂ =m₁ ) (let)...(ii) and slope line joining centres of the circles is ( aligned f₁-f₂ g₁-g₂ & =m₂ (let) m₁ m₂ & =- g₁-g₂ f₁-f₂ f₁-f₂ g₁-g₂ =-1 aligned ) Hence,

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