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AP EAMCET201825 Apr 2018Morning ShiftMathematicsHyperbolaActual

If the eccentricity of a hyperbola is 5 3 , then the eccentricity of its conjugate hyperbola is

Options

  1. A5 3
  2. B5 4
  3. C5 2
  4. D8 5

Correct answer

B. 5 4

Step-by-step solution

Let the eccentricity of hyperbola and conjugate hyperbola be e 1   &   e 2 respectively. Then, 1 e 1 2 + 1 e 2 2 = 1 ⇒ 1 5 3 2 + 1 e 2 2 = 1 ⇒ 9 25 + 1 e 2 2 = 1 ⇒ 1 e 2 2 = 1 - 9 25 ⇒ 1 e 2 2 = 16 25 ⇒ e 2 = ± 5 4 But, eccentricity of hyperbola is never less than one. Hence, e 2 = 5 4 .

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