A) \[\sqrt{\frac{7}{8}}\]
B) \[\sqrt{\frac{6}{17}}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[\sqrt{\frac{6}{11}}\]
E) \[\sqrt{\frac{6}{7}}\]
Correct Answer: E
Solution :
The equation of conic is \[\frac{{{(x+2)}^{2}}}{7}+{{(y-1)}^{2}}=14\] \[\Rightarrow \] \[\frac{{{(x+2)}^{2}}}{7\times 14}+\frac{{{(y-1)}^{2}}}{14}=1\] Here,\[{{a}^{2}}=7\times 14\]and \[{{b}^{2}}=14\] We know that, \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1-\frac{{{b}^{2}}}{4{{b}^{2}}}}\] \[=\sqrt{1-\frac{1}{7}}=\sqrt{\frac{6}{7}}\]
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