A) \[\sqrt{3}\]
B) \[\frac{4}{3}\]
C) \[\frac{4}{\sqrt{3}}\]
D) \[\frac{2}{\sqrt{3}}\]
Correct Answer: D
Solution :
Given \[\frac{2{{b}^{2}}}{a}=8\] .... (1) 2b = ae .... (2) we know \[{{b}^{2}}={{a}^{2}}({{e}^{2}}-1)\] .... (3) substitute\[\frac{b}{a}=\frac{e}{2}\]from (2) in (3) \[\Rightarrow \]\[\frac{{{e}^{2}}}{4}={{e}^{2}}-1\]\[\Rightarrow \]\[4=3{{e}^{2}}\]\[\Rightarrow \]\[e=\frac{2}{\sqrt{3}}\]
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