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JEE Main20199 Jan 2019Evening ShiftMathematicsHyperbolaActual

A hyperbola has its centre at the origin, passes through the point 4 , 2 and has transverse axis of length 4 along the x - a x i s . Then the eccentricity of the hyperbola is:

Options

  1. A3
  2. B3 2
  3. C2 3
  4. D2

Correct answer

C. 2 3

Step-by-step solution

Equation of hyperbola having tranverse axis along x - a x i s is x 2 a 2 - y 2 b 2 = 1 From the given information, equation of hyperbola can be taken as x 2 4 - y 2 b 2 = 1 , since a = 2 Since it passes through 4 ,   2 , Hence b 2 = 4 3 Now e = 1 + b 2 a 2 =   1 + 1 3 = 2 3

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