Question

The length of the transverse axis of the hyperbola $3x^2-4y^2=3$ is

• A. $\frac{8\sqrt{2}}{\sqrt{3}}$
• B. $\frac{16\sqrt{2}}{\sqrt{3}}$
• C. $\frac{3}{32}$
• D. $\frac{64}{3}$

Answer 1

The correct option is A $\frac{8\sqrt{2}}{\sqrt{3}}$

$Formulaused$
$lengthoftransverseaxisof\frac{x^2}{a^2}-\frac{y^2}{b^2}=1is$
$2a$
$Given$
$3x^2-4y^2=32$
$\Rightarrow \frac{x^2}{32/3}-\frac{y^2}{8}=1$
$a^2=\frac{32}{3},b^2=8$
$a=\frac{4\sqrt{2}}{\sqrt{3}},b=2\sqrt{2}$
$lengthoftransverseaxis=2a$
$=\frac{8\sqrt{2}}{\sqrt{3}}$