Stage 30 · Analytic Geometry

30.7.5 Eccentricity Unifies the Three Curves

30.7 The Parabola and a Unified View of Conic Sections

Point 5 of 6

30.7.5 Eccentricity Unifies the Three Curves

Core idea

With the same single e: less than 1 is an ellipse, equal to 1 is a parabola, and greater than 1 is a hyperbola.

Module goal. Introduce the parabola and, through equal point-line distance and eccentricity, thread all three curves into one system, wrapping up the coordinate method.
eastmath.com · 30.7 The Parabola and a Unified View of Conic Sections · 30.7.5 Eccentricity Unifies the Three Curves