Question

If the length of the latus rectum and the length of transverse axis of a hyperbola are \( 4\sqrt{3} \) and \( 2\sqrt{3} \) respectively, then the equation of the hyperbola is:

• A. \( \frac{x^2}{3} - \frac{y^2}{4} = 1 \)
• B. \( \frac{x^2}{3} - \frac{y^2}{9} = 1 \)
• C. \( \frac{x^2}{6} - \frac{y^2}{9} = 1 \)
• D. \( \frac{x^2}{6} - \frac{y^2}{3} = 1 \)
• E. \( \frac{x^2}{3} - \frac{y^2}{6} = 1 \)

Hint:

Always identify whether the given length is the "axis" ($2a$) or the "semi-axis" ($a$). Squaring the semi-axis gives you the denominator for the equation.

Answer 1

Answer: (E)