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AP EAMCET202315 May 2023Morning ShiftMathematicsHyperbolaActual

If is the acute angle between the tangents drawn from the point (2,3) to the hyperbola 5 x^2-6 y^2-30=0 , then =

Options

  1. A4
  2. B3 4
  3. C4 3
  4. D2

Correct answer

C. 4 3

Step-by-step solution

Given equation of ellipse x^2 6 - y^2 5 =1 Let equation of tangent y=m x+c It passes through (2,3) i.e c=3-2 m By condition of tangency. aligned & c^2=a^2 m^2-b^2 c^2=6 m^2-5 & m^2+6 m-7=0 (from (i)) & m=1,-7 aligned Now, = | 1+7 1-7 |= 8 6 = 4 3 .

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