If the eccentricity of a hyperbola is frac{5} | vedclass

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(B) Let the eccentricity of the hyperbola be $e_1$ and the eccentricity of its conjugate hyperbola be $e_2$. Then,the relation between them is given b

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$\frac{5}{4}$

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(B) Let the eccentricity of the hyperbola be $e_1$ and the eccentricity of its conjugate hyperbola be $e_2$. Then,the relation between them is given by $\frac{1}{e_1^2} + \frac{1}{e_2^2} = 1$. Given $e_1 = \frac{5}{3}$,we substitute this value into the equation: $\frac{1}{(\frac{5}{3})^2} + \frac{1}{e_2^2} = 1$ $\Rightarrow \frac{9}{25} + \frac{1}{e_2^2} = 1$ $\Rightarrow \frac{1}{e_2^2} = 1 - \frac{9}{25}$ $\Rightarrow \frac{1}{e_2^2} = \frac{16}{25}$ $\Rightarrow e_2^2 = \frac{25}{16}$ Since the eccentricity must be greater than $1$,we take the positive root: $e_2 = \frac{5}{4}$.

If the eccentricity of a hyperbola is $\frac{5}{3}$,then the eccentricity of its conjugate hyperbola is

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