A) \[\frac{3}{2}\]
B) \[\frac{2}{\sqrt{3}}\]
C) 2
D) \[\sqrt{3}\]
Correct Answer: B
Solution :
Let the equation of hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}\,-\,\frac{{{y}^{2}}}{{{b}^{2}}}\,=\,1\] Given \[2a=4\] \[\Rightarrow \,\,\,a=2\] It passes through \[\left( 4,\text{ }2 \right)\] \[\therefore \,\,\,\,\frac{16}{4}\,-\,\frac{4}{{{b}^{2}}}\,\,\,=1\,\,\,\Rightarrow \,\,{{b}^{2}}\,=\,\frac{4}{3}\] \[e\,\,=\,\,\sqrt{1+\frac{{{b}^{2}}}{{{a}^{2}}}}\,\,=\,\,\sqrt{1+\frac{4/3}{4}}\] \[=\,\,\sqrt{1+\frac{1}{3}}\,\,=\,\,\frac{2}{\sqrt{3}}\]
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