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. $6$
• C. $\frac{24}{7}$
• D. $\frac{24}{5}$
• E. $\frac{12}{7}$

Answer 1

Answer: (D)

$\frac{24}{5}$

Given, $e=\frac{5}{4}$

Focus of the hyperbola is $(ae,0)$

$\Rightarrow (\frac{5a}{4},0)$

Equation of focal chord is $2x+3y-6=0$

Focus lies on the focal chord:

$2(\frac{5a}{4},0)+3\left(0\right)-6=0\Rightarrow \frac{5a}{2}=6\Rightarrow a=\frac{12}{5}$

Length of transverse axis $=2a=\frac{24}{5}$.