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AP EAMCET2009MathematicsCircle

The equation of the circle which passes through the origin and cuts orthogonally each of the circles x^2+y^2-6 x+8=0 and x^2+y^2-2 x-2 y=7 is

Options

  1. A3 x^2+3 y^2-8 x-13 y=0
  2. B3 x^2+3 y^2+8 x+29 y=0
  3. C3 x^2+3 y^2+8 x+29 y=0
  4. D3 x^2+3 y^2-8 x-29 y=0

Correct answer

B. 3 x^2+3 y^2+8 x+29 y=0

Step-by-step solution

Let the required equation of circle be x^2+y^2+2 g x+2 f y=0 . Since, the above circle cuts the given circles orthogonally. aligned & 2(-3 g)+2 f(0)=8 & & 2 g=- 8 3 & and & -2 g-2 f=-7 & & 2 f=+7+ 8 3 = 29 3 & aligned Required equation of circle is or aligned & x^2+y^2- 8 3 x+ 29 3 y=0 & 3 x^2+3 y^2-8 x+29 y=0 aligned

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