If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 ,
Question:

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13 , then the eccentricity of the hyperbola is :-

1. 2

2. $\frac{13}{6}$

3. $\frac{13}{8}$

4. $\frac{13}{12}$

Correct Option: , 4

Solution:

$2 \mathrm{~b}=5$ and $2 \mathrm{ae}=13$

$b^{2}=a^{2}\left(e^{2}-1\right) \Rightarrow \frac{25}{4}=\frac{169}{4}-a^{2}$

$\Rightarrow \mathrm{a}=6 \Rightarrow \mathrm{e}=\frac{13}{12}$