Question

The length of transverse axis of the hyperbola $3x^2-4y^2=32$ 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

Answer: (A)

If the equation of hyperbola is
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1,$ then length of the transverse axis is
$2a.$ The given equation can be written as
$\frac{x^2}{32/3}-\frac{y^2}{8}=1.$
Here $a^2=32/3,b^2=8$
$\therefore$ The length of transverse axis
$=2a$
$=2\sqrt{\frac{32}{3}}=8\sqrt{\frac{2}{3}}$