Q210 / 270 · NDA 2016 (Phase 2) · Mathematics

What is the eccentricity of rectangular hyperbola?

  • Correct answer
    A
    $\sqrt{2}$
  • B
    $\sqrt{3}$
  • C
    $\sqrt{5}$
  • D
    $\sqrt{6}$

Solution

Here, $b^2=a^2\left(e^2-1\right)$ For rectangular hyperbola : $a=b$ $\begin{aligned} & \Rightarrow b^2=b^2\left(e^2-1\right) \\ & \Rightarrow e^2-1=1 \\ & \Rightarrow e^2=2 \Rightarrow e= \pm \sqrt{2} \end{aligned}$ For hyperbola, $\mathrm{e} \gt 1$. Hence, $\mathrm{e}=\sqrt{2}$

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

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