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AP EAMCET202315 May 2023Evening ShiftMathematicsCircleActual

The distance between the centres of similitude of the circles x^2+y^2+6 x-8 y+16=0 and x^2+y^2-2 x-2 y+1=0 is

Options

  1. A15 4
  2. B5 4
  3. C5 2
  4. D15 2

Correct answer

A. 15 4

Step-by-step solution

Given circles x^2+y^2+6 x-8 y+16=0 and x^2+y^2-2 x-2 y+1=0 (x+3)^2+(y-4)^2=3^2,(x-1)^2+(y-1)^2=1^2 So C₁=(-3,4), C₂=(1,1), r₁=3 & r₂=1 Let internal centre P= ( 3(1,1)+1(-3,4) 1+3 )= (0, 7 4 ) external centre Q= ( 3(1,1)-1(-3,4) 3-1 )= ( 6 2 , -1 2 )= (3, -1 2 ) Now P Q= (0-3)^2+ ( 7 4 + 1 2 )^2 = 9+ 81 16 = 225 16 = 15 4

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