A) \[\frac{8\sqrt{2}}{\sqrt{3}}\]
B) \[\frac{16\sqrt{2}}{\sqrt{3}}\]
C) \[\frac{3}{32}\]
D) \[\frac{64}{3}\]
Correct Answer: A
Solution :
The given equation may be written as \[\frac{{{x}^{2}}}{32/2}-\frac{{{y}^{2}}}{8}=1\] or\[\frac{{{x}^{2}}}{{{\left( 4\sqrt{2}/\sqrt{3} \right)}^{2}}}-\frac{{{y}^{2}}}{{{(2\sqrt{2})}^{2}}}=1\]. Comparing the given equation with\[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], we get \[{{a}^{2}}={{\left( \frac{4\sqrt{2}}{\sqrt{3}} \right)}^{2}}\] or \[a=\frac{4\sqrt{2}}{\sqrt{3}}.\] Therefore length of transverse axis of a hyperbola \[=2a=2\times \frac{4\sqrt{2}}{\sqrt{3}}=\frac{8\sqrt{2}}{\sqrt{3}}.\]
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