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AP EAMCET · Maths · Circle

The angle between the circles \(x^2+y^2+4 x-14 y+28=0\) and \(x^2+y^2-12 x-6 y-4=0\) is

  1. A \(60^{\circ}\)
  2. B \(\cos ^{-1} \frac{3}{35}\)
  3. C \(45^{\circ}\)
  4. D \(\cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\cos ^{-1} \frac{3}{35}\)

Step-by-step Solution

Detailed explanation

\(g_1 = 2, f_1 = -7, c_1 = 28\) \(g_2 = -6, f_2 = -3, c_2 = -4\) \(r_1 = \sqrt{g_1^2 + f_1^2 - c_1} = \sqrt{2^2 + (-7)^2 - 28} = \sqrt{4 + 49 - 28} = \sqrt{25} = 5\) \(r_2 = \sqrt{g_2^2 + f_2^2 - c_2} = \sqrt{(-6)^2 + (-3)^2 - (-4)} = \sqrt{36 + 9 + 4} = \sqrt{49} = 7\)…