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:-

• A. $2$
• B. $\frac{13}{6}$
• C. $\frac{13}{8}$
• D. $\frac{13}{12}$

Answer 1

The correct option is D $\frac{13}{12}$

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