Question

If the eccentricity of the hyperbola $\frac {x^2}{a^2}-\frac {y^2}{b^2}=1$ is $\frac {5}{4}$ and $2x + 3y -6 = 0$ is a focal chord of the hyperbola, then the length of transverse axis is equal to

• A. $\frac {12}{5}$
• B. $\frac {24}{5}$
• C. $\frac {6}{5}$
• D. $\frac {5}{24}$

Answer 1

Answer: (B)

$\frac {24}{5}$

Answer 2

Given hyperbola has focus $(a e, 0)$ which will lie on $2 x+3 y-6=0$ as it is focal chord.
$\therefore 2 a e-6=0$
$\Rightarrow a e=3$
$\Rightarrow a \times \frac{5}{4}=3$
$\left[\because e=\frac{5}{4}\right]$
$\Rightarrow a=\frac{12}{5}$
$\therefore$ Length of transverse axis $=2 a$
$=2 \times \frac{12}{5}=\frac{24}{5}$