Question

\(S\) and \(T\) are the foci of an ellipse and \(B\) is the end point of the minor axis. If \(S T B\) is equilateral triangle, the eccentricity of the ellipse is
(A) \(\frac{1}{4}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{2}{3}\)

Answer 1

Ans: (C)
Hint : \(2 \mathrm{ae}=\sqrt{(\mathrm{ae})^{2}+\mathrm{b}^{2}} \Rightarrow \frac{\mathrm{b}^{2}}{\mathrm{a}^{2}}=3 \mathrm{e}^{2} \Rightarrow \mathrm{e}^{2}=\frac{1}{4} \Rightarrow \mathrm{e}=\frac{1}{2}\)

Answer 2

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Answer 3

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