If the eccentricity of a hyperbola is sqrt{3} | vedclass

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(C) Let $e$ and $e^{\prime}$ be the eccentricities of a hyperbola and its conjugate hyperbola respectively.We know that the relationship between them

Vedclass · Accepted Answer

$\sqrt{\frac{3}{2}}$

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(C) Let $e$ and $e^{\prime}$ be the eccentricities of a hyperbola and its conjugate hyperbola respectively.We know that the relationship between them is given by $\frac{1}{e^2} + \frac{1}{(e^{\prime})^2} = 1$.Given that $e = \sqrt{3}$,we have $e^2 = 3$.Substituting this into the formula: $\frac{1}{3} + \frac{1}{(e^{\prime})^2} = 1$.$\frac{1}{(e^{\prime})^2} = 1 - \frac{1}{3} = \frac{2}{3}$.Therefore,$(e^{\prime})^2 = \frac{3}{2}$,which implies $e^{\prime} = \sqrt{\frac{3}{2}}$.

If the eccentricity of a hyperbola is $\sqrt{3}$,then the eccentricity of its conjugate hyperbola is:

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