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A hyperbola having its centre at the origin is passing through the point (5,2) and has transverse axis of length 8 along the X -axis. Then the eccentricity of its conjugate hyperbola is

Options

  1. A13 3
  2. B13 3
  3. C13 2
  4. D13 2

Correct answer

C. 13 2

Step-by-step solution

Let equation of hyperbola is x^2 a^2 - y^2 b^2 =1 Given, 2 a =8 a =4 It passes through (5,2) Hence, on solving we get, b = 8 3 Now, eccentricity of its conjugate hyperbola is = a ^2+ b ^2 ~b ^2 = 13 2

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