COMEDK · Maths · 12. Circle
If the circles \(x^{2}+y^{2}+2 g x+2 f y=0\) and \(x^{2}+y^{2}+2 g^{\prime} x+2 f^{\prime} y=0\) touch each other, then
- A \(f g=f^{\prime} g^{\prime}\)
- B \(f^{\prime} g=f g^{\prime}\)
- C \(f f^{\prime}=g g^{\prime}\)
- D None of these
Answer & Solution
Correct Answer
(B) \(f^{\prime} g=f g^{\prime}\)
Step-by-step Solution
Detailed explanation
For given condition, \[ \begin{aligned} \frac{2 g}{2 g^{\prime}} &=\frac{2 f}{2 f^{\prime}} \\ \Rightarrow \quad f^{\prime} &=f g^{\prime} \end{aligned} \]
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