Definition of an ellipse

Overview

Locus of points with PF₁ + PF₂ = 2a (constant).

Explanation

An ellipse is the set of points whose distances to foci F₁, F₂ sum to constant 2a (with 2a > |F₁F₂|).
|F₁F₂| = 2c, b² = a² − c², eccentricity e = c/a (0 ≤ e < 1).
Smaller e → rounder; larger e → flatter.

How to use

Drag P on the ellipse; PF₁ + PF₂ stays 2a. Adjust a, c for shape.

Knowledge points

• Conics
• Ellipses
• High school