Q98 / 160 · AP EAMCET 2006 · Mathematics

If the eccentricity of a hyperbola is $\sqrt{3}$; then the eccentricity of its conjugate hyperbola is :

  • A
    $\sqrt{2}$
  • B
    $\sqrt{3}$
  • Correct answer
    C
    $\sqrt{\frac{3}{2}}$
  • D
    $2 \sqrt{3}$

Solution

Let $e$ and $e^{\prime}$ are the eccentricities of a hyperbola and its conjugate hyperbola. We know that $\frac{1}{e^2}+\frac{1}{\left(e^{\prime}\right)^2}=1$ $\Rightarrow \quad \frac{1}{3}+\frac{1}{\left(e^{\prime}\right)^2}=1$ $\Rightarrow \quad \frac{1}{\left(e^{\prime}\right)^2}=\frac{2}{3} \Rightarrow e^{\prime}=\sqrt{\frac{3}{2}}$

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

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