# If a hyperbola has length of its conjugate axis

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. (1) $\frac{13}{12}$

2. (2) 2

3. (3) $\frac{13}{6}$

4. (4) $\frac{13}{8}$

Correct Option: 1

Solution:

$\therefore$ Conjugate axis $=5$

$\therefore \quad 2 b=5$

Distance between foci $=13$

$2 a e=13$

Then, $b^{2}=a^{2}\left(e^{2}-1\right)$

$\Rightarrow a^{2}=36$

$\therefore \quad a=6$

$a e=\frac{13}{2} \Rightarrow e=\frac{13}{12}$