AP EAMCET · Maths · Circle
If the circles \(x^2+y^2-4 x+2 f y+1=0\) and \(x^2+y^2+\) \(2 \mathrm{gx}-4 \mathrm{y}-1=0\) cut orthogonally, then \(\mathrm{r}_1^2+\mathrm{r}_2^2-8=\)
- A \(\mathrm{g}^2\)
- B \(-\mathrm{f}^2\)
- C \(2 \mathrm{~g}^2\)
- D \(-2 \mathrm{f}^2\)
Answer & Solution
Correct Answer
(C) \(2 \mathrm{~g}^2\)
Step-by-step Solution
Detailed explanation
Let \(S_1: x^2+y^2-4 x+2 f y+1=0\) ...(i) \(S_2: x^2+y^2+2 g x-4 y-1=0\) ...(ii) \(\begin{aligned} & \mathrm{g}_1=2, \mathrm{f}_1=\mathrm{f}, \mathrm{c}_1=1 \\ & \mathrm{~g}_2=\mathrm{g}, \mathrm{f}_2=2, \mathrm{c}_2=-1\end{aligned}\) \(\because\) Circle (i) \& (ii) are…
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