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In an ellipse, OB is a semi-minor axis, and F, F' are the two foci. If the angle FBF' is a right angle, find the eccentricity of the ellipse.
- 1/sqrt(2)
- 1/2
- 1/sqrt(3)
- 1/3
Correct answer: 1/sqrt(2)
Solution
BF = BF' = a, and right angle at B gives FF' = a*sqrt(2); since FF' = 2ae, we get 2ae = a*sqrt(2), so e = 1/sqrt(2).
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