A) \[\frac{2\sqrt{2}}{3}\]
B) \[\frac{\sqrt{5}}{3}\]
C) \[\frac{8}{9}\]
D) \[\frac{2}{3}\]
Correct Answer: A
Solution :
\[\frac{2}{3}=\frac{\pi {{a}^{2}}-\pi ab}{\pi {{a}^{2}}}=1-\frac{b}{a}=1-\sqrt{1-{{e}^{2}}}\]\[\Rightarrow {{e}^{2}}=\frac{8}{9}\Rightarrow e=\frac{2\sqrt{2}}{3}\]
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