Question

In a hyperbola e = $\frac{9}{4}$ and the distance between the directrices is 3. Then the length of Transverse axis is

• A. $\frac{27}{2}$
• B. $\frac{27}{8}$
• C. $\frac{27}{4}$
• D. $\frac{17}{4}$

Answer 1

The correct option is C

$\frac{27}{4}$

e = $\frac{9}{4}$

$\frac{2a}{\left(\frac{9}{4}\right)}=3$ $\Rightarrow$ 8a = 27 $\Rightarrow$ a = $\frac{27}{8}$

$2a=\frac{27}{4}$