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AP EAMCET202319 May 2023Morning ShiftMathematicsHyperbolaActual

Let e be the eccentricity of the ellipse x ^2 4 + y ^2 9 =1 . If 1 e is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola is

Options

  1. A4 3
  2. B3 5
  3. C4 5
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Given ellipse x^2 4 + y^2 9 =1 Since b>a i.e. 9>4 . Hence aligned & e= 1 b h^2-a^2 = 1 3 9-4 & e= 5 3 aligned Let e_H= 1 e = 3 5 be the eccentricity of hyperbola and e_C be the eccentricity of the conjugate hypérbola. We know that, for a hyperbola- aligned & 1 e_H^2 + 1 e_C^2 =1 ( 5 3 )^2+ 1 e_C^2 =1 & e_C=3 / 2 aligned

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