Conics Flashcards
Up/down Parabola equation
(x-h)²=4p(y-k)
Left/right parabola equation
(y-k)²=4p(x-h)
Vertex parabola
(h,k)
Up/down focus parabola
(h, k+p)
Left/right focus parabola
(h+p, k)
Up/down directrix parabola
y=k-p
left/right directrix parabola
x=h-p
Horizontal ellipse equation
(x-h)²/a² + (y-k)²/b²=1
vertical ellipse equation
(x-h)²/b² + (y-k)²/a²=1
center ellipse
(h,k)
Foci ellipse horizontal
(c,0) (-c,0)
foci ellipse vertical
(0,c) (0,-c)
vertical equation hyperbola
(y-k)²/a² - (x-h)²/b² =1
center hyperbola
(h,k)
foci hyperbola vertical
(c, 0) (-c,0)
foci hyperbola horizontal
(0,c) (0,-c)
finding c ellipse
a-b
finding c hyperbola
a+b
How to complete the square to find the equation
group x and y
factor
complete the square in each group
add/subtract the number taken out by the number that completes the square
make it equal 1
Rotation B²-4AC < 0
Ellipse
Rotation B²-4AC =0
Parabola
Rotation B²-4AC > 0
Hyperbola
Rotation angle
tan (2theta) =B/A-C
if A-C=0… Theta =
45 degrees
