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. \( \frac{12}{7} \)

Hint:

To find the focus from a focal chord equation, simply find where the line intersects the major/transverse axis (usually by setting $y=0$ or $x=0$).

Answer 1

The Correct Option is D