A) \[\frac{1}{2}\]
B) \[\frac{2\sqrt{2}-1}{2}\]
C) \[\sqrt{2}-1\]
D) \[\frac{\sqrt{2}-1}{2}\]
Correct Answer: C
Solution :
\[2ae=\frac{1}{2}\left( \frac{2{{b}^{2}}}{a} \right)\]\[\Rightarrow \]\[2ae=\frac{{{b}^{2}}}{a}\]\[\Rightarrow \]\[2e=\frac{{{b}^{2}}}{{{a}^{2}}}\] also\[{{e}^{2}}=1-\frac{{{b}^{2}}}{{{a}^{2}}}\Rightarrow {{e}^{2}}=1-2e\Rightarrow e=\sqrt{2}-1\]
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