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

$\Rightarrow a^{2}=36$

$\therefore \quad a=6$

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

 

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