Question

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

• A. $\frac{12}{5}$
• B. $\frac{12}{7}$
• C. $\frac{24}{5}$
• D. $\frac{24}{7}$

Answer 1

The correct option is C

$\frac{24}{5}$

The hyperbola is of the form
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

The transverse axis of the hyperbola is along the x-axis. Given that 2x + 3y-6=0 is a focal chord. Let (c,0) be the focus.
$\Rightarrow 2c+0-6=0\Rightarrow c=3Given,e=\frac{5}{4}a=\frac{c}{e}=\frac{12}{5}$

The length of the transverse axis is $2a=\frac{24}{5}$