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 either \(g=\frac{3}{2}\) or \(f \neq 2\)
- B either \(\mathrm{g} \neq \frac{3}{4}\) or \(\mathrm{f}=\frac{1}{2}\)
- C either \(g=\frac{3}{4}\) or \(f=2\)
- D either \(g=\frac{1}{2}\) or \(f=\frac{3}{4}\)
Answer & Solution
Correct Answer
(C) either \(g=\frac{3}{4}\) or \(f=2\)
Step-by-step Solution
Detailed explanation
Radical axis \(L: S_1 - \frac{1}{2}S_2 = 0\) \((x^2+y^2+2gx+2fy+c) - (x^2+y^2+\frac{3}{2}x+4y+c) = 0\) \((2g - \frac{3}{2})x + (2f - 4)y = 0\) Alternatively, using \(2S_1 - S_2 = 0\) to avoid fractions directly: \((2x^2+2y^2+4gx+4fy+2c) - (2x^2+2y^2+3x+8y+2c) = 0\)…
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