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AP EAMCET20226 Jul 2022Evening ShiftMathematicsHyperbolaActual

Let x^2+y^2=16 be the equation of the auxiliary circle of a hyperbola x^2 a^2 - y^2 b^2 =1 and let (4 2 , 3) be a point on the hyperbola. Then, the eccentricity of the hyperbola is

Options

  1. A5 / 4
  2. B5 / 3
  3. C4 / 3
  4. D2

Correct answer

A. 5 / 4

Step-by-step solution

The auxiliary circle of a hyperbola x^2 a^2 - y^2 b^2 =1 is x^2+y^2=a^2 . a^2=16 a=4 The hyperbola passes through (4 2 , 3) aligned & 32 16 - 9 b^2 & =1 & 2-1 & = 9 b^2 b^2=9 & e & = 1+ b^2 a^2 = 1+ 9 16 = 5 4 aligned

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