The eccentricity of a rectangular hyperbola i | vedclass

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(C) rectangular hyperbola is defined as a hyperbola where the lengths of the transverse and conjugate axes are equal,i.e.,$a = b$.For a hyperbola $\fr

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$\sqrt{2}$

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(C) rectangular hyperbola is defined as a hyperbola where the lengths of the transverse and conjugate axes are equal,i.e.,$a = b$.For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$,the eccentricity $e$ is given by the formula $e = \sqrt{1 + \frac{b^2}{a^2}}$.Substituting $a = b$ into the formula,we get $e = \sqrt{1 + \frac{a^2}{a^2}} = \sqrt{1 + 1} = \sqrt{2}$.Therefore,the eccentricity of a rectangular hyperbola is $\sqrt{2}$.

The eccentricity of a rectangular hyperbola is

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