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The equation a(x² + y² + 2y + 1) = (x - 2y + 3)² represents an ellipse precisely when a lies in the interval (b, infinity). Find the value of b.
- 5
- 1
- 4
- 25
Correct answer: 5
Solution
The left side is a*(distance from (0,-1))²; the right is (sqrt(5))² * (distance to line x - 2y + 3 = 0)². So eccentricity e satisfies e² = 5/a. Ellipse needs e < 1, i.e. 5/a < 1, a > 5, so b = 5.
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