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What is the eccentricity of rectangular hyperbola?
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Verified Answer
The correct answer is:
$\sqrt{2}$
Here, $b^{2}=a^{2}\left(e^{2}-1\right)$
For rectangular hyperbola : $a=b$ $\Rightarrow b^{2}=b^{2}\left(e^{2}-1\right)$
$\Rightarrow e^{2}-1=1$
$\Rightarrow e^{2}=2 \Rightarrow e=\pm \sqrt{2}$
For hyper bola, $\mathrm{e}>1$
Hence, $\mathrm{e}=\sqrt{2}$
For rectangular hyperbola : $a=b$ $\Rightarrow b^{2}=b^{2}\left(e^{2}-1\right)$
$\Rightarrow e^{2}-1=1$
$\Rightarrow e^{2}=2 \Rightarrow e=\pm \sqrt{2}$
For hyper bola, $\mathrm{e}>1$
Hence, $\mathrm{e}=\sqrt{2}$
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