alleryStart learning →For every point on an ellipse, which quantity built from the two foci stays constant?
AThe sum of the two distances
BThe product of the two distances
CThe larger of the two distances
DThe ratio of the two distances
Answer & Solution
Correct answer: A. The sum of the two distances
1. Pin a string at two fixed points and trace it taut with a pencil.
2. The string length never changes, so the two distances always add to the same total.
3. That constant total is what defines an ellipse, not a product, a ratio or a maximum.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.1 The Ellipse_
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