Question

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

• A. $\frac{5}{3}$
• B. $\frac{5}{4}$
• C. $\frac{5}{2}$
• D. $\frac{8}{5}$

Answer 1

Answer: (B)

Eccentricity of given hyperbola $=\frac{5}{3}$
Let, eccentricity of its conjugate hyperbola $=e$
So, $\frac{1}{{\left(\frac{5}{3}\right)}^2}+\frac{1}{e^2}=1\left[\begin{array}{c}\because \text{ relationship between }\\ \text{ eccentricity is }\frac{1}{e_1^2}+\frac{l}{e_2^2}=1\end{array}\right]$
$\Rightarrow \frac{9}{25}+\frac{1}{e^2}=1$
$\Rightarrow \frac{1}{e^2}=1-\frac{9}{25}$
$\Rightarrow \frac{1}{e^2}=\frac{16}{25}$
$\Rightarrow e^2=\frac{25}{16}$
$\Rightarrow e=\frac{5}{4}$
Hence, eccentricity of conjugate hyperbola $=\frac{5}{4}$