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AP EAMCET202420 May 2024Evening ShiftMathematicsCircleActual

The radical centre of the circles x^2+y^2+2 x+3 y+1=0 , x^2+y^2+x-y+3=0, x^2+y^2-3 x+2 y+5=0 is

Options

  1. A(- 7 38 , 6 19 )
  2. B( 6 19 , 14 19 )
  3. C( 14 19 , 6 19 )
  4. D( 2 19 , 3 19 )

Correct answer

C. ( 14 19 , 6 19 )

Step-by-step solution

S ₁ x^2+y^2+2 x+3 y+1=0 aligned & S ₂ x^2+y^2+x-y+3=0 & ~S ₃ x^2+y^2-3 x+2 y+5=0 aligned aligned & S ₁- S ₂=0 x+4 y-2=0 (i) & ~S ₂- S ₃=0 4 x-3 y-2=0 (ii) aligned Solving (i) and (ii) we get radical centre = ( 14 19 , 6 19 )

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