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If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

Options

A1 2
B2 - 1
C2 - 1 2
D2 2 - 1 2

Correct answer

B. 2 - 1

Step-by-step solution

2 a e = 1 2 × 2 b 2 a 2 e = b 2 a 2 We know that e = 1 - b 2 a 2 e = 1 - 2 e e 2 = 1 - 2 e e 2 + 2 e - 1 = 0 - 2 ± 4 + 4 2 = - 2 ± 2 2 2 - 1 + 2     &   - 1 - 2 ∴       e = 2 - 1

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