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AP EAMCET2015MathematicsCircle

The locus of centres of the circles, which cut the circles x^2+y^2+4 x-6 y+9 and x^2+y^2-5 x+4 y+2=0 orthogonally, is

Options

  1. A3 x+4 y-5=0
  2. B9 x-10 y+7=0
  3. C9 x+10 y-7=0
  4. D9 x-10 y+11=0

Correct answer

B. 9 x-10 y+7=0

Step-by-step solution

Let the circle be Cuts the circle aligned & x^2+y^2+4 x-6 y+9=0 and & x^2+y^2-5 x+4 y+2=0 aligned orthogonally. For circle aligned & x^2+y^2+4 x-6 y+9=0 & 2 (g₁ g₂+f₁ f₂ )=c₁+c₂ & 2[(g)(-2)+(f)(3)]=c+9 aligned For circle, aligned & x^2+y^2-5 x+4 y+2=0 & 2 [(g) ( 5 2 )+(f)(-2) ]=c+2 aligned On subtracting Eq. (iii) from Eq. (ii), we get aligned & -9 g+10 f=7 & 9 g-10 f=-7 aligned Replace g and f by x and y to get the locus of centre, aligned & 9 x-10 y=-7 & 9 x-10 y+7=0 aligned

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