The farther the foci sit from the center the flatter it gets, with e=c/a between 0 and 1, looking more like a rugby ball as it nears 1.
Module goal. Introduce the ellipse from the constant sum of distances to two fixed points, build its standard equation, and read off its geometric properties.
eastmath.com · 30.5 The Ellipse: A Circle Pulled Flat · 30.5.4 Eccentricity: How Flat the Ellipse Is