Pre-Calc Conics

x2 + y2 = 0

graph is a point

x*2 = 1

graph is 2 parallel lines

B*2 - 4AC > 0

hyperbola

B*2 - 4AC < 0

ellipse

parabola

one square term

(x-h)*2 = 4p(y-k)

parabola
up/down

(y-k)*2 = 4p(x-h)

parabola
left/right

(x-h)2/a2 + (y-k)2/b2 = 1

ellipse
horizontal (a = left to right)

(x-h)2/b2 + (y-k)2/a2 = 1

ellipse
vertical (a = up/down)

x2 = y2

2 intersecting lines, y = x and y = -x

ellipse

a > b
x is ALWAYS on the RIGHT
plus sign
foci = minus sign (c2 = a2 - b*2)
major (a) / minor axis (b)

Hyperbola

a*2 is always first
minus sign
foci plus sign
transverse (x)/conjugate (y) axis
asym: y-k = +/- m(x-h)

(x-h)2/a2 - (y-k)2/b2 = 1

horizontal hyperbola

(y-k)2/a2 - (x-h)2/b2

vertical hyperbola

eccentricity

c/a

c

distance from the center to the foci