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An ellipse has vertices at (3, -1) and (3, 9). Where is its center?
AAt the point (3, 4)
BAt the point (3, 5)
CAt the point (0, 4)
DAt the point (3, 8)
Answer & Solution
Correct answer: A. At the point (3, 4)
1. The two vertices share the x-coordinate 3, so the major axis is vertical.
2. The center is halfway between them, which is the midpoint of the two points.
3. Averaging the y-coordinates gives negative 1 plus 9, all over 2, which is 4.
4. So the center is (3, 4), not (3, 5), which comes from averaging the wrong pair.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_
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