Useful information about ellipses:
(note: a is the length of the major
semiaxis, b is the length of the minor
semiaxis, c is the distance from the
focus to the
center, and a²-b²=c²)
Horizontal major axis Horizontal minor axis
Standard Form: (x-h)²/a²+(y-k)²/b²=1 (x-h)²/b²+(y-k)²/a²=1
Eccentricity: e=c/a (e<1, e=0 ⇒ circle) e=c/a (e<1, e=0 ⇒ circle)
Length of latera recta: l=2b²/a l=2b²/a
Directrices: x=±a²/c+h y=±a²/c+k
Vertices: (h±a,k±b) (h±b,k±a)
Foci: (h±c,k) (h,k±c)
Parametric Form: x′=asin(t) or x′=acos(t) x′=bsin(t) or x′=bcos(t)
y′=bcos(t) y′=bsin(t) y′=acos(t) y′=asin(t)
See also: