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S and $T$ are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is
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Verified Answer
The correct answer is:
$\frac{1}{2}$
Hints : $\frac{\mathrm{b}}{\mathrm{ae}}=\sqrt{3} ; \quad \mathrm{b}=\sqrt{3} \mathrm{ae}$
$$
\mathrm{e}^2=\frac{\mathrm{a}^2-3 \mathrm{a}^2 \mathrm{e}^2}{\mathrm{a}^2}=1-3 \mathrm{e}^2 ; \quad 4 \mathrm{e}^2=1 \Rightarrow \mathrm{e}=\frac{1}{2}
$$
$$
\mathrm{e}^2=\frac{\mathrm{a}^2-3 \mathrm{a}^2 \mathrm{e}^2}{\mathrm{a}^2}=1-3 \mathrm{e}^2 ; \quad 4 \mathrm{e}^2=1 \Rightarrow \mathrm{e}=\frac{1}{2}
$$
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