Question

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

• A. $\sqrt{\frac{4}{3}}$
• B. $\sqrt{\frac{3}{2}}$
• C. $\sqrt{\frac{5}{3}}$
• D. $\sqrt{\frac{5}{4}}$

Answer 1

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

Given, $\frac{2b^2}{a}=a\Rightarrow \frac{b^2}{a^2}=\frac{1}{2}$
Thus required eccentricity is $=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{\frac{3}{2}}$