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)

$\frac{24}{5}$

We have eccentricity $=\frac{5}{4}$

The focus( considering one only) of the hyperbola is $(ae,0)$

So focal chord will satisfy the focus

$\Rightarrow 2\left(ae\right)+3\left(0\right)=6$

$\Rightarrow ae=3\Rightarrow a=\frac{3}{3}=\frac{12}{5}$

Hence length of tranverse axes $=2a=\frac{24}{5}$