I'm trying to understand the proof for eccentricity; I can get
about halfway through it. The problem I'm having is summarized
below If e<1, you get the equation of an ellipse of the form The
foci of an ellipse are at a distance c from the center, where
This shows that It follows from equations 4 and 5 that the
eccentricity is given by If someone could help explain how is
derived, or really what it means I'd be so grateful. I'm using
Calculus Early Transcendentals 6th Ed. by Stewart (Ch. 10, Sect.
6).