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An ellipse in standard form has minor axis (along the y-axis) of length 4/sqrt(3). If this ellipse is tangent to the line x + 6y = 8, find its eccentricity.
- (1/2)sqrt(11/3)
- sqrt(5/6)
- (1/3)sqrt(11/3)
- (1/2)sqrt(5/3)
Correct answer: (1/2)sqrt(11/3)
Solution
With b² = 4/3 and the tangency condition giving a², e² = 1 - b²/a² yields e = (1/2)sqrt(11/3).
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