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AP EAMCET202317 May 2023Evening ShiftMathematicsCircleActual

The distance of the origin from the external centre of similitude for the circles x^2+y^2-8 x-10 y-8=0 and x ^2+ y ^2+2 x -2 y -2=0 is

Options

  1. A3 26 5
  2. B290 9
  3. C290 5
  4. D26 3

Correct answer

A. 3 26 5

Step-by-step solution

Let S ₁: x^2+y^2-8 x-10 y-8=0 aligned & C ₁=(4,5) & r₁= 16+25+8 =7 & and S ₂: x^2+y^2+2 x-2 y-2=0 & C ₂=(-1,1) & r₂= 1+1+2 =2 aligned Using section formula, external centre of similitude is: Q ( r₁ x₂-x₁ r₂ r₁-r₂ , r₁ y₂-r₂ y₁ r₁-r₂ ) ( -7 1-4 2 7-2 , 7 1-2 5 7-2 ) (-3,- 3 5 ) Distance from origin to Q is D = (-3)^2+ ( -3 5 )^2 = 1+ 1 25 (3)= 3 5 26

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