Conic Sections Formulas ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ), Exercises of Pre-Calculus

Equations of Parabola: 1) Parabola opens up: 4 vertex = , ; focus = ,. ; directrix: 2) Parabola opens down: 4 vertex = , ; focus = ,. ; directrix:.

Typology: Exercises

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Conic Sections Formulas
2
2
Equations of Parabola:
1) Parabola opens up: 4
vertex = , ; focus = , ; directrix:
2) Parabola opens down: 4
vertex = , ; focus = , ; directrix:
x h p y k
h k h k p y k p
x h p y k
h k h k p y k

2
2
3) Parabola opens right: 4
vertex = , ; focus = , ; directrix:
4) Parabola opens left: 4
vertex = , ; focus = , ; directrix:
p
y k p x h
h k h p k x hp
y k p x h
h k h p k x hp
pf3

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Conic Sections Formulas

2

2

Equations of Parabola:

  1. Parabola opens up: 4 vertex = , ; focus = , ; directrix:
  2. Parabola opens down: 4 vertex = , ; focus = , ; directrix:

x h p y k h k h k p y k p x h p y k h k h k p y k

2

2

  1. Parabola opens right: 4 vertex = , ; focus = , ; directrix:
  2. Parabola opens left: 4 vertex = , ; focus = , ; directrix:

p y k p x h h k h p k (^) xhp y k p x h h k h p k xhp

   

     

   

2 2 2 2 2 2 2

2 2 2 2 2

Ellipse Elongated Horizontally

Equation: 1 ;

Center of Ellipse: ,

Vertices: ,

Foci: ,

Ellipse Elongated Vertically

Equation: 1;

x h y k a b

a b

a b c

h k

h a k

h c k

x h y k a b

b a

a

     

2 2

Center of Ellipse: ,

Vertices: ,

Foci: ,

b c

h k

h k a

h k c