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Points A(-1, 0) and B(2, 0) lie on the x-axis. A point M (not on the x-axis) moves so that angle MBA = 2*angle MAB. M traces a conic. Which property of this conic is correct?
- Eccentricity equals 2
- Coordinates of vertices are (+/-3, 0)
- Length of latus rectum equals 6
- Equations of directrices are x = +/-1/2
Correct answer: Eccentricity equals 2
Solution
The angle condition makes M trace a branch of a hyperbola with foci A and B; the constant difference of focal radii gives 2a = 3/2 with 2c = 3, so e = c/a = 2.
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