A) \[\frac{1}{\sqrt{2}}\]
B) \[\frac{1}{2}\]
C) \[\frac{\sqrt{3}}{2}\]
D) \[\frac{3}{4}\]
E) \[\frac{3}{5}\]
Correct Answer: C
Solution :
We know that length of latusrectum of an ellipse\[=\frac{2{{b}^{2}}}{a}\]and length of its minor axis\[=2b\] \[\therefore \] \[\frac{2{{b}^{2}}}{a}=b\Rightarrow 2b=a\] Also, \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1-\frac{{{b}^{2}}}{4{{b}^{2}}}}\] \[=\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}\]
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