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  4. Find the eccentricity of the hyperbola whose latus rectum 12 and semi-conjugate axis is 2 √3.

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

Conic Sections

Solution:

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