A) \[\frac{1}{4}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{2}\]
D) \[\sqrt{\frac{3}{2}}\]
E) \[\frac{1}{\sqrt{2}}\]
Correct Answer: C
Solution :
In \[\Delta BOT,\] \[\frac{b}{ae}=\tan 60{}^\circ \Rightarrow b=ae\sqrt{3}\] \[\therefore \] \[e=\sqrt{1-\frac{{{b}^{2}}}{{{a}^{2}}}}=\sqrt{1-\frac{{{a}^{2}}{{e}^{2}}3}{{{a}^{2}}}}\] \[\Rightarrow \] \[{{e}^{2}}=1-3{{e}^{2}}\Rightarrow 4{{e}^{2}}=1\] \[\Rightarrow \] \[{{e}^{2}}=\frac{1}{4}\] \[\Rightarrow \] \[e=\pm \frac{1}{2}\]You need to login to perform this action.
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