JEE Main 2024 Mathematics question
If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is:
Answer: (B)
Solution
2b = (1/2)(2ae), so ae = 2b. Then 4b²/a² = e², i.e. 4(1 − e²) = e², so 5e² = 4 and e = 2/√5.