Conics Flashcards
Right opening parabola
(y-k)2 = 4a(x-h)
Left opening parabola
(y-k)2 = -4a(x-h)
Standard parabola
(x-k)2 = 4a(y-k)
Inverted parabola
(x-k)2 = -4a(y-k)
Standard parabola focus
(h+a, k)
Inverted parabola focus
(h-a, k)
Right opening parabola foci
(h, k+a)
Left opening parabola foci
(h, k-a)
Horizontal parabola directrix
x = h±a (a is negative when opening left)
Vertical parabola directrix
x = k±a (a is negative when opening down)
Horizontal ellipse
(x-h)2/a2 + (y-k)2/b2 = 1
Vertical ellipse
(x-h)2/b2 + (y-k)2/a2 = 1
Vertical ellipse foci
(h, k±c)
Horizontal ellipse foci
(h±c, k)
Horizontal ellipse vertices
(h±a, k)
Vertical ellipse vertices
(h, k±a)
b
Length from center of an ellipse to the edge of the ellipse along the minimal axis
a
Distance from vertex to focus and/or directrix of a parabola
OR
Distance from center of an ellipse to either vertex along the maximal axis
h
x-coordinate of the vertex of a parabola
OR
x-coordinate of the center of an ellipse
k
y-coordinate of the vertex of a parabola
OR
y-coordinate of the center of an ellipse
c
b2 = a2 + c2
(might be some kind of rectum but we don’t need to know that)
finishing the square
group terms by variable
add b2/4a to each variable group
a = leading coefficient (make this 1 before completing)
b = coefficient of x
remove negative terms from each group
you can figure it out from here
latus rectum parabola
line through the focus parallel to the directrix
points that define the latus rectum parabola
2a away from the focus (remember the l.r. is parallel to the directrix)
