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AP EAMCET201921 Apr 2019Evening ShiftMathematicsHyperbolaActual

A hyperbola with centre at ( 0 , 0 ) has its transverse axis along X -axis whose length is 12 . If ( 8 , 2 ) is a point on the hyperbola, then its eccentricity is

Options

  1. A8 7
  2. B2 2 7
  3. C3 7
  4. D9 7

Correct answer

B. 2 2 7

Step-by-step solution

Consider the equation of the hyperbola be x 2 a 2 - y 2 b 2 = 1 It is given that the centre of the hyperbola is 0 , 0 and its transverse axis is along x -axis and its length is 12 . 2   a = 12 a = 6 Substitute this value in the equation of a hyperbola. x 2 6 2 - y 2 b 2 = 1 The above equation passes through the point   8 , 2 8 2 6 2 - 2 2 b 2 = 1 64 36 - 4 b 2 = 1 After simplification, b = 6 7 The equation of hyperbola becomes, x 2 6 2 - y 2 6 7 2 = 1 x 2 36 - 7 y 2 36 = 1 The eccentricity of a hyperbola

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