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AP EAMCET202123 Aug 2021Morning ShiftMathematicsCircleActual

Which circle among the following bisects the circumference of the circle x^2+y^2-8 x-6 y+23=0 ?

Options

  1. Ax^2+y^2-6 x-4 y+9=0
  2. Bx^2+y^2+6 x+4 y-9=0
  3. Cx^2+y^2-6 x+4 y-9=0
  4. Dx^2+y^2+6 x-4 y+9=0

Correct answer

A. x^2+y^2-6 x-4 y+9=0

Step-by-step solution

Given circle, x^2+y^2-8 x-6 y+23=0 Centre of this circle is (4,3) . If the equation of radical axis of circle S₁ and S₂ passes through (4,3) , then S₂ bisect the circumference of S₁ . Option (a) Let S₂=x^2+y^2-6 x-4 y+9=0 Then, equation of radical axis (L) is aligned L: S₁-S₂ & =0 L: (x^2+y^2-8 x-6 y+23 ) & - (x^2+y^2-6 x-4 y+9 ) & =0 L:-2 x-2 y+14 & =0 L: x+y-7=0 aligned Check whether (4,3) satisfy equation L . LHS (4) + (3) -7=0= RHS x^2+y^2-6 x-4 y+9=0 bisect the circumference of circle x^2+y^2-8 x-6 y+23=0 Simi

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