Question

If the distance between the foci and the distance between the two directricies of a hyperbola are in the ratio $5:4$ , then the eccentricity of the hyperbola is :

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

Answer 1

The correct option is D $\frac{\sqrt{5}}{2}$

Let the hyperbola be $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$\left|\frac{2ae}{2\times \frac{a}{e}}\right|=\frac{5}{4}\Rightarrow e^2=\frac{5}{4}\Rightarrow e=\frac{\sqrt{5}}{2}$