TS EAMCET · Maths · Circle
Suppose the circle \(S: x^2+y^2+2 g x+2 f y+c=0 \text { cuts }\) orthogonally the two circles \(S^{\prime}: x^2+y^2-4 x-6 y+11=0\) and \(S^{\prime \prime}: x^2+y^2-10 x-4 y+21=0\). If the centre of \(S=0\) lies on the bisector of the angle between the positive coordinate axes, then \(2 g+2 f+c=\)
- A 12
- B 8
- C 4
- D 0
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
\(x^2+y^2+2 g x+2 f y+c=0\) cuts orthogonally the circle \(x^2+y^2-4 x-6 y+11=0\) and \(x^2+y^2-10 x-4 y+21=0\) \(\therefore \quad-4 g-6 f=c+11\) \(\ldots(\mathrm{i})\) and \(\quad-10 g-4 f=c+21\) \(\ldots(\mathrm{ii})\) Centre of circle \(x^2+y^2+2 g x+2 f y+c=0\) is lie in…
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