AP EAMCET · Maths · Circle
If the circles \(x^2+y^2-2 \lambda x-2 y-7=0\) and \(3\left(x^2+y^2\right)-8 x+29 y=0\) are orthogonal, then \(\lambda=\)
- A 4
- B 3
- C 2
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
For \(x^2+y^2-2 \lambda x-2 y-7=0\): \(g_1 = -\lambda, f_1 = -1, c_1 = -7\). For \(x^2+y^2-\frac{8}{3} x+\frac{29}{3} y=0\): \(g_2 = -\frac{4}{3}, f_2 = \frac{29}{6}, c_2 = 0\). \(2g_1 g_2 + 2f_1 f_2 = c_1 + c_2\) \(2(-\lambda)(-\frac{4}{3}) + 2(-1)(\frac{29}{6}) = -7 + 0\)…
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