Question

Find the eccentricity of a hyperbola whose latus rectum is half of its transverse axis.

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

Answer 1

The correct option is B $\sqrt{\frac{3}{2}}$

$\mathrm{Given}\mathrm{that},\frac{2b^2}{a}=a2b^2=a^2$
$\mathrm{So},\mathrm{eccentricity}e=\frac{\sqrt{a^2+b^2}}{a}e=\frac{\sqrt{2b^2+b^2}}{\sqrt{2}b}e=\frac{\sqrt{3}b}{\sqrt{2}b}e=\sqrt{\frac{3}{2}}$