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AP EAMCET2013MathematicsCircle

If the circle x^2+y^2+4 x-6 y+c=0 bisects the circumference of the circle x^2+y^2-6 x+4 y-12=0 , then c is equal to

Options

  1. A16
  2. B24
  3. C-42
  4. D-62

Correct answer

D. -62

Step-by-step solution

The common chord of the given circle is array cc & S₁-S₂=0 & (x^2+y^2+4 x-6 y+c ) & - (x^2+y^2-6 x+4 y-12 )=0 & 10 x-10 y+c+12=0 array Since, circle x^2+y^2+4 x+6 y+c=0 bisects the circumference of the circle. x^2+y^2-6 x+4 y-12=0 Therefore, Eq. (i) passes through the centre of second circle i.e., (3,-2) aligned & & 10(3)-10(-2)+c+12 & =0 & & 30+20+c+12 & =0 & & c & =-62 aligned

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