If S and S' are foci of the ellipse <span class="math-tex">\(\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1,\)</span> B is the end of the minor axis and BSS' is an equilateral triangle, then the eccentricity of the ellipse is
B = (0, b), S = (ae, 0), S' = (−ae, 0).
BS = \(\sqrt{a^2e^2 + b^2} = a\) (since \(b^2 = a^2(1 - e^2)\)), and SS' = 2ae.
The triangle is equilateral, so \(a = 2ae\), giving \(e = \frac{1}{2}\).
Answer: (A) \(\frac{1}{2}\)
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