AP EAMCET · Maths · Circle
If the circles \(x^2+y^2+2 \alpha x+2 y-8=0\) and \(x^2+y^2-2 x\) \(+\alpha y-14=0\) intersect orthogonally, then the distance between their centres is
- A \(\sqrt{242}\)
- B \(\sqrt{970}\)
- C \(\sqrt{629}\)
- D \(\sqrt{541}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{629}\)
Step-by-step Solution
Detailed explanation
\(S_1 \equiv x^2+y^2+2 \alpha x+2 y-8=0\) \(\begin{aligned} & \Rightarrow \quad\left(g_1, f_1, c_1\right)=(\alpha, 1,-8) \\ & S_2 \equiv x^2+y^2-2 x+\alpha y-14=0 \\ & \Rightarrow \quad\left(g_2, f_2, c_2\right)=\left(-1, \frac{\alpha}{2},-14\right) \end{aligned}\) \(S_1\) and…
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