AP EAMCET · Maths · Circle
If the radical axis of the circles
\(x^2+y^2+2 g x+2 f y+c=0\) and
\(2 x^2+2 y^2+3 x+8 y+2 c=0\) touches the circle \(x^2+y^2+2 x+2 y+1=0\), then
- A \(g=\frac{3}{4}\) or \(f=2\)
- B \(g \neq \frac{3}{4}, f=2\)
- C \(g=\frac{3}{4}\) or \(f \neq 2\)
- D \(g=\frac{2}{5}\) or \(f=1\)
Answer & Solution
Correct Answer
(A) \(g=\frac{3}{4}\) or \(f=2\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Let point } P(a, b) \\ & \qquad \begin{array}{l} S_1(a, b)=S_2(a, b) \\ \Rightarrow a^2+b^2+2 g a+2 f b+c=a^2+b^2+\frac{3}{2} a+4 b+c=0 \\ a\left(2 g-\frac{3}{2}\right)+b(2 f-4)=0 \end{array} \end{aligned} \] this is the locus of radical axis. So,…
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