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For every point on a hyperbola, which quantity built from the two foci stays constant?
AThe sum of the distances
BThe product of the distances
CThe average of the distances
DThe difference of the distances
Answer & Solution
Correct answer: D. The difference of the distances
1. A hyperbola has two foci, exactly like an ellipse does.
2. What is held fixed here is the difference of the two distances, not their sum.
3. That single change of sum to difference is what splits the curve into two branches.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 8 "Analytic Geometry", section 8.2 The Hyperbola_
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