A) \[\frac{5}{14}\]
B) \[\frac{4}{5}\]
C) \[\frac{3}{5}\]
D) \[\frac{2}{5}\]
Correct Answer: C
Solution :
\[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{(25/4)}=1\]. Here, \[a=2,\,\,b=5/2\] \[\therefore b>a\], therefore \[{{a}^{2}}={{b}^{2}}(1-{{e}^{2}})\] Þ\[4=\frac{25}{4}(1-{{e}^{2}})\]Þ \[\frac{16}{25}=1-{{e}^{2}}\] Þ \[{{e}^{2}}=1-\frac{16}{25}=\frac{9}{25}\], \ \[e=\frac{3}{5}\] .
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