Useful information about hyperbolas:
(note: c is the distance from the
center to the
focus, a is the distance from the
vertex to the
center, and a²+b²=c²)
Horizontal transverse axis Horizontal conjugate axis
Standard Form: (x-h)²/a²-(y-k)²/b²=1 (y-k)²/a²-(x-h)²/b²=1
Eccentricity: e=c/a (e>1) e=c/a (e>1)
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)
Asymptotes: y=k±(b/a)(x-h) y=k±(a/b)(x-h)
Parametric Form: x′=asec(t) x′=btan(t)
y′=btan(t) y′=asec(t)
See also: