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AP EAMCET202421 May 2024Morning ShiftMathematicsCircleActual

If a direct common tangent drawn to the circles x^2+y^26 x+4 y+9=0 and x^2+y^2+2 x-2 y+1=0 touches the circles at A and B , then AB =

Options

  1. A9
  2. B16
  3. C4 6
  4. D2 6

Correct answer

D. 2 6

Step-by-step solution

aligned & x^2+y^2-6 x+4 y+9=0 & (x-3)^2+(y+4)^2=4 ...(i) & and x^2+y^2+2 x-2 y+1=0 & (x+1)^2+(y-1)^2=1 ...(ii) & C₁=(3,-4), C₂=(-1,1), r₁=2, r₂=1 aligned So, C ₁ C ₂=5 |r₁-r₂ |=1 Length of direct common tangent = ( C ₁ C ₂ )^2- (r₁-r₂ )^2 AB =2 6

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