If the eccentricity of a hyperbola is $\dfrac{5}{4}$, then find the eccentricity of its conjugate hyperbola.

If the eccentricity of a hyperbola is (5)/(4), then find the eccentricity of its conjugate hyperbola.

Question 3 of 6

\dfrac{5}{4}

Yanam BieapBIEAP Intermediate Board 2025Subjective· 2mImportance★★★★★

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If $e_1,e_2$ are the eccentricities of a hyperbola and its conjugate hyperbola, then $\dfrac{1}{e_1^2}+\dfrac{1}{e_2^2}=1$ .

Given $e_1=\dfrac{5}{4}$ :

$\frac{1}{(5/4)^2}+\frac{1}{e_2^2}=1 \implies \frac{16}{25}+\frac{1}{e_2^2}=1 \implies \frac{1}{e_2^2}=\frac{9}{25}.$

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