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AP EAMCET201822 Apr 2018Evening ShiftMathematicsCircleActual

If a circle S passing through the point (3,4) cuts the circle x^2+y^2=36 orthogonally, then the locus of the centre of S is

Options

  1. Ax^2+y^2-6 x-8 y+11=0
  2. B6 x+8 y-61=0
  3. Cx^2+y^2-8 x-6 y+11=0
  4. D6 x+8 y+11=0

Correct answer

B. 6 x+8 y-61=0

Step-by-step solution

Let the circle is x^2+y^2+2 g x+2 f y+c=0 , having centre (-g,-f) , since it passes through the point (3,4) And circle is intersecting the other circle aligned & x^2+y^2=36 orthogonally, so & 2 g(0)+2 f(0)=c-36 aligned From Eqs. (i) and (ii) -6 g-8 f=61, Now, on taking locus of point (-g,-f) , we are getting 6 x+8 y-61=0 .

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