A) \[\frac{1}{2}\]
B) \[\frac{\sqrt{3}}{2}\]
C) \[\frac{3}{4}\]
D) \[\frac{\sqrt{15}}{4}\]
Correct Answer: B
Solution :
[b] Length of latus rectum of an ellipse is \[\frac{2{{b}^{2}}}{a}\] Where b is semi minor axis and a is semi- major axis. As given, \[\frac{2{{b}^{2}}}{a}=b\] \[\Rightarrow 2b=a\Rightarrow \frac{b}{a}=\frac{1}{2}\] We know that eccentricity \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}\] \[=\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2}\]
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