The eccentricity of a rectangular hyperbola is

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Aicharya · Accepted Answer

The general equation of a hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, where $a$ represents the transverse of hyperbola and $b$ represents the conjugate of the hyperbola. The eccentricity of a hyperbola is $e=\frac{\sqrt{a^2+b^2}}{a} \cdots(1)$. Since a rectangular hyperbola is defined as a hyperbola whose transverse axis is identical to its conjugate axis, $a=b$. Substitute $a=b$ into (1). $\begin{aligned} & e=\frac{\sqrt{a^2+b^2}}{a} \ & \Rightarrow e=\frac{\sqrt{a^2+a^2}}{a} \ & \Rightarrow e=\frac{\sqrt{2 a^2}}{a} \ & \Rightarrow e=\frac{\sqrt{2} a}{a} \ & \Rightarrow e=\sqrt{2} \end{aligned}$

The eccentricity of a rectangular hyperbola is

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