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AP EAMCET20226 Jul 2022Evening ShiftMathematicsCircleActual

The radical centre of the circles x^2+y^2+3 x+2 y+1=0x^2+y^2-x+6 y+5=0 and x^2+y^2+5 x-8 y+15=0 is

Options

  1. A(3,2)
  2. B(-3,-2) .
  3. C(2,3)
  4. D(-2,-3)

Correct answer

A. (3,2)

Step-by-step solution

aligned & Let S₁: x^2+y^2+3 x+2 y+1=0 & S₂: x^2+y^2-x+6 y+5=0 & S₃: x^2+y^2+5 x-8 y+15=0 aligned Let (x, y) be the radical centre, then S₁-S₂=0 and aligned & S₂-S₃=0 & 4 x-4 y-4=0 and -6 x+14 y-10=0 & x=y+1 and 3 x-7 y+5=0 & 3(y+1)-7 y+5=0 3 y+3-7 y+5=0 & -4 y+8=0 & y=2 and x=2+1=3 aligned Radical centre is (3,2) .

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