AP EAMCET · Maths · Circle
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 \(g=\frac{3}{8}\) or \(f=1\)
- B \(g=\frac{2}{3}\) or \(f=3\)
- C \(g=\frac{1}{2}\) or \(f=1\)
- D \(g=\frac{3}{4}\) or \(f=2\)
Answer & Solution
Correct Answer
(D) \(g=\frac{3}{4}\) or \(f=2\)
Step-by-step Solution
Detailed explanation
Equation of radical axis is \(\left(2 g-\frac{3}{2}\right) x+(2 f-4) y=0\) Since \(x\) and \(y\) axis touch the circle \(x^2+y^2+2 x+2 y+1=0\) \(y=\left(\frac{2 g-\frac{3}{2}}{2 f-4}\right) x\) touches the circle and passing through the origin.…
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