Question

If the eccentricity of the hyperbola
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\text{is}d\frac{5}{4}\text{and}2x+3y-6=0$
is the 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

The correct option is B $\frac{24}{5}$

$\because \text{focus lies on the}2x+3y-6=0\therefore ae=3\Rightarrow a=\frac{12}{5}$
length of transverse axis$=2a=\frac{2\times 12}{5}=\frac{24}{5}$