AP EAMCET · Maths · Circle
If the circles \(x^2+y^2+k x+4 y+2=0\) and \(2\left(x^2+y^2\right)-4 x-3 y+k=0\) cut orthogonally, then \(k=\)
- A \(\frac{-10}{3}\)
- B \(\frac{10}{3}\)
- C \(\frac{5}{3}\)
- D \(\frac{-5}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{-10}{3}\)
Step-by-step Solution
Detailed explanation
\(g_1 = \frac{k}{2}, f_1 = 2, c_1 = 2\) \(g_2 = -1, f_2 = -\frac{3}{4}, c_2 = \frac{k}{2}\) \(2g_1g_2 + 2f_1f_2 = c_1+c_2\) \(2(\frac{k}{2})(-1) + 2(2)(-\frac{3}{4}) = 2 + \frac{k}{2}\) \(-k - 3 = 2 + \frac{k}{2}\) \(-k - \frac{k}{2} = 2 + 3\) \(-\frac{3k}{2} = 5\)…
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