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  4. 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 :-

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Q. 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 :-

JEE MainJEE Main 2019Conic Sections

Solution:

$2b = 5$ and $2ae = 13$
$b^{2} =a^{2} \left(e^{2} -1\right) \Rightarrow \frac{25}{4} = \frac{169}{4} -a^{2} $
$ \Rightarrow a =6 \Rightarrow e = \frac{13}{12} $