Question

If the length of latus rectum of a hyperbola $\frac{x^2}{k}-\frac{y^2}{25}=-1$ is $\frac{22}{5}$ units, then its $e$ (eccentricity) is

• A. $\frac{7}{3}$
• B. $\frac{7}{5}$
• C. $\frac{6}{5}$
• D. $\frac{7}{2}$

Answer 1

The correct option is C $\frac{6}{5}$

Given, latus rectum $=\frac{22}{5}$ units
$\Rightarrow \frac{2a^2}{b}=\frac{22}{5}$
$\Rightarrow \frac{2k}{5}=\frac{22}{5}$
$\Rightarrow k=11$
then
$a^2=11$ and $b^2=25$

$e=\sqrt{\frac{a^2+b^2}{b^2}}=\sqrt{\frac{11+25}{25}}$
$\Rightarrow e=\frac{6}{5}$