Question

Find the eccentricity of the hyperbola whose latus rectum $12$ and semi-conjugate axis is $2\sqrt{3}$.

Answer 1

Answer: 2.00

$\frac{2b^2}{a}=12$ and $b=2\sqrt{3}$
$\Rightarrow a=2$
$\Rightarrow a^2=4$
$\Rightarrow b^2=12$
Now $e=\sqrt{1+\frac{12}{4}}=2$