A) \[\frac{\sqrt{5}+1}{2}\]
B) \[9{{x}^{2}}+5{{y}^{2}}-30y=0\]
C) \[\frac{\sqrt{5}}{2}\]
D) \[\frac{\sqrt{3}}{2}\]
Correct Answer: B
Solution :
\[\frac{2{{b}^{2}}}{a}=2ae\]Þ \[{{b}^{2}}={{a}^{2}}e\]or\[e=\frac{{{b}^{2}}}{{{a}^{2}}}\] Also \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\]or \[{{e}^{2}}=1-e\]or \[{{e}^{2}}+e-1=0\] Therefore\[e=\frac{-1\pm \sqrt{5}}{2}\]. As\[e<1,\]\ \[e=\frac{\sqrt{5}-1}{2}\].
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