Question

The length of transverse axis of the hyperbola $ 3{{x}^{2}}-4{{y}^{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}} $