If `S\ a n d\ S '` are two foci of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1\ a n d\ B` is and end of the minor axis such that `"Delta"B S S '` is equilateral, then write the eccentricity of the ellipse.

Options

A. `3/4`
B. `7`
C. `4/5`
D. `1/2`

Answer

`1/2`

Explanation

For ellipse `frac(x^(2))(a^(2))+frac(y^(2))(b^(2))=1`, distance between foci is `2ae`, where e is eccentricity of an ellipse.

So, 2 ae will be length of side of equilateral triangle `triangle BSS’`

And semi minor axis will be height of this triangle.

We know that height of equilateral triangle is `frac(sqrt(3))(2)` time s its side.

So, According to given condition,

`b=frac(sqrt(3))(2) 2ae`


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