Question

In a hyperbola the latusrectum equals to semitransverse axis,then its eccentricity is

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

Answer 1

The correct option is D

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

$\frac{2b^2}{a}$ = a $\Rightarrow$ $\frac{b^2}{a^2}$ = $\frac{1}{2}$

e = $\sqrt{1+\frac{b^2}{a^2}}$ = $\sqrt{1+\frac{1}{2}}$ = $\sqrt{\frac{3}{2}}$