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AP EAMCET202422 May 2024Morning ShiftMathematicsCircleActual

If x-4=0 is the radical axis of two orthogonal circles out of which one is x^2+y^2=36 , then the centre of the other circles is

Options

  1. A(8,0)
  2. B(9,0)
  3. C(6,0)
  4. D(12,0)

Correct answer

B. (9,0)

Step-by-step solution

Let equation of other circle be aligned & S^ x^2+y^2+2 g x+2 f y+c=0 & S x^2+y^2=36 aligned x^ -4=0 is radicalaxis S^ =x^2+y^2-36+k(x-4) As circles are orthogonal aligned & 2 g(0)+2 f(0)=4 k -36-36 k=-18 & S^ =x^2+y^2-18 x-36=0 aligned So centre is (9,0) .

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