A) \[\frac{8}{17}\]
B) \[\frac{15}{17}\]
C) \[\frac{9}{17}\]
D) \[\frac{2\sqrt{2}}{17}\]
E) \[\frac{13}{17}\]
Correct Answer: B
Solution :
Given, \[a=\frac{17}{8}b\] \[\because \] \[{{b}^{2}}={{a}^{2}}(1-{{e}^{2}})\] \[\Rightarrow \] \[{{b}^{2}}={{\left( \frac{17}{8}b \right)}^{2}}(1-{{e}^{2}})\] \[\Rightarrow \] \[{{b}^{2}}=\frac{289}{64}{{b}^{2}}(1-{{e}^{2}})\] \[\Rightarrow \] \[\frac{64}{289}=1-{{e}^{2}}\] \[\Rightarrow \] \[{{e}^{2}}=1-\frac{64}{286}=\frac{289-64}{289}\] \[\Rightarrow \] \[{{e}^{2}}=\frac{225}{289}\] \[\Rightarrow \] \[e=\frac{15}{17}\]
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