AP EAMCET · Maths · Circle
If a system of circles pass through \((2,3)\) and cuts the circle \(x^2+y^2=12\) orthogonally, then the equation of the locus of the centres of that system of circles, is
- A \(4 x+6 y-13=0\)
- B \(4 x+6 y-25=0\)
- C \(6 x+4 y-25=0\)
- D \(6 x+4 y-13=0\)
Answer & Solution
Correct Answer
(B) \(4 x+6 y-25=0\)
Step-by-step Solution
Detailed explanation
Let the equation of the system of circles be \(x^2+y^2+2gx+2fy+c=0\). Passes through \((2,3)\): \(2^2+3^2+2g(2)+2f(3)+c=0 \implies 13+4g+6f+c=0\). Cuts \(x^2+y^2=12\) orthogonally: \(2g_1g_2+2f_1f_2=c_1+c_2\). Here, \(g_1=0, f_1=0, c_1=-12\). So,…
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