30.6.1 Where the Hyperbola Comes From: A Fixed Difference
30.6 The Hyperbola: The Path of a Constant Difference
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30.6.1 Where the Hyperbola Comes From: A Fixed Difference
Core idea
When the absolute difference of distances to the two foci stays fixed at 2a, you get two branches opening away from each other.
Module goal. Introduce the hyperbola from the constant difference of distances to two fixed points, and master its standard equation, asymptotes, and eccentricity.
eastmath.com · 30.6 The Hyperbola: The Path of a Constant Difference · 30.6.1 Where the Hyperbola Comes From: A Fixed Difference