Q41 / 160 · WBJEE 2011 · Mathematics

The eccentricity of the hyperbola \(4 x^2-9 y^2=36\) is

  • A
    \(\frac{\sqrt{11}}{3}\)
  • B
    \(\frac{\sqrt{15}}{3}\)
  • Correct answer
    C
    \(\frac{\sqrt{13}}{3}\)
  • D
    \(\frac{\sqrt{14}}{3}\)

Solution

Hints: \(\frac{x^2}{9}-\frac{y^2}{4}=1\) \(\begin{aligned} & a=3, b=2 \\ & \therefore e=\sqrt{\frac{a^2+b^2}{a^2}}=\sqrt{\frac{13}{9}}=\frac{\sqrt{13}}{3} \end{aligned}\)

Hence, the correct answer is option: 'C'.

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