Question

The eccentricity of the hyperbola whose latus rectum is equal to half of its conjugate axis is

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

Answer 1

Answer: (D)

$\frac{\sqrt{5}}{2}$

For a hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$

Latus rectum is given by $\frac{2b^2}{a}$ and

The conjugate axis is given by $2b$

According to the given condition, $\frac{2b^2}{a}=b$

$\therefore a=2b$

Eccentricity $=\sqrt{1+\frac{b^2}{a^2}}=\sqrt{1+\frac{1}{4}}$

$=\sqrt{\frac{5}{4}}$

$=\frac{\sqrt{5}}{2}$