The eccentricity of a rectangular hyperbola i | vedclass

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(D) The equation of a rectangular hyperbola is given by $x^2 - y^2 = a^2$,which can be written as $\frac{x^2}{a^2} - \frac{y^2}{a^2} = 1$. Here,the le

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$\sqrt{2}$

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(D) The equation of a rectangular hyperbola is given by $x^2 - y^2 = a^2$,which can be written as $\frac{x^2}{a^2} - \frac{y^2}{a^2} = 1$. Here,the length of the transverse axis is $2a$ and the length of the conjugate axis is $2a$. Since both axes are equal,the eccentricity $e$ is calculated as: $e = \sqrt{1 + \frac{b^2}{a^2}} = \sqrt{1 + \frac{a^2}{a^2}} = \sqrt{1 + 1} = \sqrt{2}$.

The eccentricity of a rectangular hyperbola is

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