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Pa n dQ are the foci of the ellipse (x^2...

`Pa n dQ` are the foci of the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` and `B` is an end of the minor axis. If `P B Q` is an equilateral triangle, then the eccentricity of the ellipse is `1/(sqrt(2))` (b) `1/3` (d) `1/2` (d) `(sqrt(3))/2`

A

`1//sqrt(2)`

B

`1//3`

C

`1//2`

D

`sqrt(3)//2`

Text Solution

AI Generated Solution

To solve the problem, we need to find the eccentricity of the ellipse given the conditions of the triangle formed by the foci and the endpoint of the minor axis. ### Step-by-Step Solution: 1. **Identify the Foci and the Endpoint of the Minor Axis:** - The foci of the ellipse are given by the points \( P(ae, 0) \) and \( Q(-ae, 0) \). - The endpoint of the minor axis, denoted as \( B \), is at the point \( (0, b) \). ...
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