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AP EAMCET · Maths · Circle

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

  1. A \(x^2+y^2-6 x-8 y+11=0\)
  2. B \(6 x+8 y-61=0\)
  3. C \(x^2+y^2-8 x-6 y+11=0\)
  4. D \(6 x+8 y+11=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(6 x+8 y-61=0\)

Step-by-step Solution

Detailed explanation

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 \[ \begin{aligned} & x^2+y^2=36 \text { orthogonally, so } \\ & \qquad 2 g(0)+2 f(0)=c-36 \end{aligned} \] From Eqs.…