For every point on a hyperbola, which quantity built from the two foci stays constant?

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_