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The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is

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$\frac{4}{3}$

$\frac{4}{\sqrt{3}}$

$\frac{2}{\sqrt{3}}$

$\sqrt{3}$

answer is C.

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Detailed Solution

$\frac{2 b^{2}}{a} = 8, 2 b = \frac{1}{2} 2 a e$

$\to \frac{b^{2}}{a^{2}} = a^{2} e^{2} ∴ e = \frac{2}{\sqrt{3}}$

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