# If latus rectum of the hyperbola is half of its transverse axis, then its eccentricity is Option 1) 3/2 Option 2) $\frac{\sqrt{3}}{2}$ Option 3) $\sqrt{\frac{3}{2}}$ Option 4) none of these

$\frac{2b^{2}}{a}=\frac{2b}{2}$

$\Rightarrow 2b=a$

Also, $b^{2}-a^{2} (e^{2}-1)$

$\Rightarrow \frac{1}{4} = e^{2}-1$

$\Rightarrow e^{2}=\frac{5}{4}\Rightarrow e\frac{\sqrt{5}}{2}$

Option 1)

3/2

This solution is incorrect

Option 2)

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

This solution is incorrect

Option 3)

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

This solution is incorrect

Option 4)

none of these

This solution is correct

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