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 :
Key Idea: 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 \[=2a\] \[=2\sqrt{\frac{32}{3}}=8\sqrt{\frac{2}{3}}\]
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