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A circle meets the ellipse x²/a² + y²/b² = 1 at exactly three points A, B, C. AB is a diameter of the circle and is perpendicular to the major axis of the ellipse. Given the ellipse's eccentricity is 4/5 and the diameter AB = lambda*a, find lambda.
- 18/25
- 9/25
- 36/25
- 16/25
Correct answer: 18/25
Solution
With e = 4/5, b² = a²(9/25). The geometry of a vertical-diameter circle meeting the ellipse at exactly three points yields AB = (18/25)a, so lambda = 18/25.
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