2ae=21×a2b2
2e=a2b2
We know that
e=1−a2b2
e=1−2e
e2=1−2e
e2+2e−1=0
2−2±4+4=2−2±22
-1+\sqrt{2} & -1-\sqrt{2}
∴e=2−1
If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:
Held on 11 Apr 2015 · Verified 6 Jul 2026.
21
2−1
22−1
222−1
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