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AP EAMCET2003MathematicsCircle

If the circle x^2+y^2+6 x-2 y+k=0 bisects the circumference of the circle x^2+y^2+2 x-6 y-15=0 , then k is equal to :

Options

  1. A21
  2. B-21
  3. C23
  4. D-23

Correct answer

D. -23

Step-by-step solution

Given that, S₁ x^2+y^2+6 x-2 y+k=0 and S₂ x^2+y^2+2 x-6 y-15=0 Since, S₁ bisects S₂ , then Chord of S₂= Diameter of S₁ Equation of the chord is S₁-S₂=0 (x^2+y^2+6 x-2 y+k )- (x^2+y^2+2 x-6 y-15 )=0 4 x+4 y+k+15=0 Centre of the circle of S₂=(-1,3) Since, equation of the chord passes through (-1,3) , then 4(-1)+4(3)+k+15=0 -4+12+k+15=0 k=-23

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