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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Hyperbola

NDA 2016 · Mathematics · Hyperbola

What is the eccentricity of rectangular hyperbola?

What is the eccentricity of rectangular hyperbola?

Options

  1. A2\sqrt{2}
  2. B3\sqrt{3}
  3. C5\sqrt{5}
  4. D6\sqrt{6}

Correct answer

A. 2\sqrt{2}

Step-by-step solution

Here, b2=a2(e2−1)Forb^2=a^2 \left(e²-1\right) Forrectangular hyperbola : a=b⇒b2=b2(e2−1)⇒e2−1=1⇒e2=2⇒e=±2\begin{aligned}& \Rightarrow b²=b²\left(e²-1\right) \\ & \Rightarrow e²-1=1 \\ & \Rightarrow e²=2 \Rightarrow e= \pm \sqrt{2} \end{aligned}For hyperbola, \mathrm{e} \gt1.Hence,. Hence,\mathrm{e}=\sqrt{2}
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