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TS EAMCET · Maths · Circle

If \(\theta\) is the angle between the circles \(x^2+y^2-4 x+2 y-4=0\) and \(x^2+y^2-2 x+4 y-11=0\), then \(\sin \theta=\)

  1. A \(\frac{\sqrt{47}}{24}\)
  2. B \(\frac{23}{25}\)
  3. C \(\frac{23}{24}\)
  4. D \(\frac{\sqrt{3}}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\sqrt{47}}{24}\)

Step-by-step Solution

Detailed explanation

\(g_1=-2, f_1=1, c_1=-4\) \(g_2=-1, f_2=2, c_2=-11\) \(r_1 = \sqrt{(-2)^2+1^2-(-4)} = 3\) \(r_2 = \sqrt{(-1)^2+2^2-(-11)} = 4\) \(\cos \theta = \frac{2g_1g_2+2f_1f_2-c_1-c_2}{2r_1r_2}\) \(\cos \theta = \frac{2(-2)(-1)+2(1)(2)-(-4)-(-11)}{2(3)(4)}\)…