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

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Aicharya · Accepted Answer

Eccentricity of given hyperbola $=\frac{5}{3}$ Let, eccentricity of its conjugate hyperbola $=e$ So, $\frac{1}{\left(\frac{5}{3}\right)^2}+\frac{1}{e^2}=1$ $\Rightarrow \quad \frac{9}{25}+\frac{1}{e^2}=1 \quad \Rightarrow \frac{1}{e^2}=1-\frac{9}{25}$ $\Rightarrow \quad \frac{1}{e^2}=\frac{16}{25} \Rightarrow e^2=\frac{25}{16}$ $ \Rightarrow \quad e=\frac{5}{4} $ Hence, eccentricity of conjugate hyperbola $=\frac{5}{4}$

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

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