Question

The length of the latus rectum and the length of the transverse axis of a hyperbola are $4\sqrt{3}\&2\sqrt{3}$ respectively, then the equation of the hyperbola can be

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

Answer 1

The correct option is A

$\frac{x^2}{3}-\frac{y^2}{6}=1$

Let the transverse axis be along the x-axis such that the hyperbola is of the form

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
$\text{Latus Rectum =}\frac{2b^2}{a}=4\sqrt{3}$
$\text{Also,}2a=2\sqrt{3}\Rightarrow a=\sqrt{3}$

$\frac{2b^2}{\sqrt{3}}=4\sqrt{3}\Rightarrow b^2=6$

The equation of the hyperbola is

$\frac{x^2}{3}-\frac{y^2}{6}=1$