Vector Methods, Conic Section: Ellipse
[b]Proposition:[/b] Given an ellipse in the form
[math]\;\;\;{\bf r}(t) = \cos(t) {\bf u} + λ \sin(t) {\bf v},[/math]
[math]\;\;\;\;\;\;\;\;\;\;\;{\small {\bf u}⊥ {\bf v},\;\; |{\bf u}|= |{\bf v}|,\;\; 0≤|λ|≤1}[/math],*
....to give the foci as a vector formula.
*(In other words, u, v are orthogonal (perpendicular) and u is the major axis of the ellipse).
