Conics Cheat Sheet (DRAFT) by teeswizzle

standard Form	(x-h)2 + (y-k)2 = r2
	derived from distance formula
centre	(h, k)
radius	r

horizontal transverse axis (x coeffi­cient > 0)	(x-h)2/a2 - (y-k)2/b2 = 1
vertices	(h ± a, k)
foci	(h ± c, k)
asymptote	y-k=±(­b/a­)(x-h)
------­---­---­---­---­---­---­---­---­---­---­-----
vertical transverse axis (y coeffi­cient > 0)	(y-k)2/a2 - (x-h)2/b2 = 1
vertices	(h, k ± a)
foci	(h, k ± c)
asymptote	y-k=±(­a/b­)(x-h)
------­---­---­---­---­---­---­---­---­---­---­-----
transverse axis	passes through center vertex of both parabolas
a	distance from centre to each vertex
b	point on conjugate axis, not a point on hyperbola
centre	distance from center to each focus, c2=a2+b2

vertex	(h, k)
------­---­------------­---­------~~----­-------
opens up/down	(x-h)2 = 4p(y-k)
focus	(h, k+p)
directrix	y=k-p
opens up	p > 0
opens down	p < 0
------­---­------------­---­------~~----­-------
opens right/left	(y-k)2 = 4p(x-h)
foci	(h+p, k)
directrix	x=h-p
opens right	p > 0
opens left	p < 0

horizontal major axis (a > b)	(x-h)2/a2 + (y-k)2/b2 = 1
vertices	(h ± a, k)
foci	(h ± c, k)
------­---­---­---­---­---­---­---­---­---­---­-----
vertical major axis (b > a)	(x-h)2/b2 + (y-k)2/a2 = 1
vertices	(h, k ± a)
foci	(h, k ± c)
------­---­---­---­---­---­---­---­---­---­---­-----
major axis	longer axis
minor axis	shorter axis
a	distance from centre to each vertex
b	distance from center to end of minor axis
c	distance from center to each focus, c2=a2-b2
length of minor axis	2a
length of major axis	2b