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AP EAMCET202421 May 2024Morning ShiftMathematicsCircleActual

The radius of the circle which cuts the circles x^2+y^2-4 x-4 y+7=0, x^2+y^2+4 x-4 y+6=0 and x^2+y^2+4 x+4 y+5=0 orthogonally is

Options

  1. A193 4 2
  2. B193 8
  3. C193 8
  4. D193 2 2

Correct answer

A. 193 4 2

Step-by-step solution

Let equation circle be x^2+y^2+2 g x+2 f y+c=0 It is orthogonal with x^2+y^2-4 x-4 y+7=0 aligned & 2 g(-2)+2 f(-2)=c+7 & 4 g+4 f+c=-7...(i) aligned Also orthogonal with x^2+y^2+4 x-4 y+6=0 aligned & 2 g(2)+2 f(-2)=c+6 & 4 g-4 f-c=6...(ii) aligned And orthogonal with aligned & x^2+y^2+4 x+4 y+5=0 & 2 g(2)+2 f(2)=c+5 & 4 g+4 f-c=5...(iii) aligned Solving (i), (ii) and (iii) we get aligned & c =-6, f= -1 8 , g= -1 8 & radius = g^2+f^2- C = 1 64 + 1 64 +6 = 193 4 2 aligned

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