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AP EAMCET202023 Sep 2020Morning ShiftMathematicsCircleActual

The angle between the pair of tangents drawn from 1 , 3 to the circle x 2 + y 2 - 2 x + 4 y - 11 = 0 is

Options

  1. Asin - 1 24 25
  2. Bsin - 1 7 25
  3. Ccos - 1 24 25
  4. Dtan - 1 7 24

Correct answer

A. sin - 1 24 25

Step-by-step solution

x 2 + y 2 - 2 x + 4 y - 11 = 0 Let the angle between tangents = 2 θ Now, tan θ = r L T where r is the radius of the circle and L T is the length of tangent from the given point. Here L T = S 1 = 1 2 + 3 2 - 2 + 12 - 11 = 3 r = 1 2 + 2 2 + 11 = 4 i.e. tan θ = 4 3 ⇒ tan 2 θ = 2 × 4 3 1 - 16 9 = 8 3 - 7 9 = - 24 7 sin 2 θ = 24 25 ⇒ 2 θ = sin - 1 ( 24 25 )

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