If *S* and *S*' are two foci of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and *B* is an end of the minor axis such that ∆*BSS*' is equilateral, then write the eccentricity of the ellipse.

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#### Solution

\[\text{ We know that the focal distance of a point B }(0, b) \text{ is } a \pm e . 0 = a\]

\[\text{ i . e } . SB = SB' = a\]

`therefore SB + S B^' = 2a `

`"Since" ∆ {BSS}^' \"is equilateral, we have":`

`SB = S S^' = S^' B = 2ae`

\[ \Rightarrow 2ae + 2ae = 2a\]

\[ \Rightarrow 4ae = 2a\]

\[ \Rightarrow e = \frac{2}{4}\]

\[ \Rightarrow e = \frac{1}{2}\]

Is there an error in this question or solution?

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