A) \[\sqrt{2}\]
B) \[2\sqrt{3}\]
C) \[\sqrt{3}\]
D) \[3\sqrt{3}\]
Correct Answer: A
Solution :
Given, hyperbola is \[{{x}^{2}}-{{y}^{2}}=4\] \[\Rightarrow \] \[\frac{{{x}^{2}}}{4}-\frac{{{y}^{2}}}{4}=1\] Here, \[{{a}^{2}}=4,{{b}^{2}}=4\] Eccentricity, \[e=\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}\] \[=\sqrt{1+\frac{4}{4}}\] \[=\sqrt{1+1}=\sqrt{2}\] Alternate Method: Since, the given curve is rectangular hyperbola, so its eccentricity is\[\sqrt{2}\].
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