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If S\ a n d\ S ' are two foci of the ell...

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.

A

`3/4`

B

`7`

C

`4/5`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
`1/2`
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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Knowledge Check

  • Let S and T be the foci of the ellipse (x^(2))/(a^(2))+(y^(2))/(bh^(2)) = 1 and be an end of the minor axis. If STB is an equilateral triangle, then eccentricity of the ellipse is

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    `1/2`
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    `sqrt(3/2)`

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