EllipseEasy
Question
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of theellipse is :
Options
A.
B.√2 − 1
C.1/2
D.
Solution
2ae = b2/a ⇒ 2a2e = b2 = a2(1− e2)
⇒ 2e = 1 − e2
⇒ (e + 1)2 = 2
⇒ e = √2 − 1
⇒ 2e = 1 − e2
⇒ (e + 1)2 = 2
⇒ e = √2 − 1
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