Alg II 10­2 Parabolas ­ End.notebook
May 08, 2017
10-2 Parabolas
A parabola is the set of all points in a plane that are the same distance from a fixed line (directrix) and a fixed point not on the line (focus).
The position of a parabola can be vertical (open up or down) or they can be horizontal (open right or left).
horizontal parabola
vertical
parabola
Vertical Parabolas (vertex at the origin)
equation:
focus:
(0, c)
directrix:
y = −c
1
Alg II 10­2 Parabolas ­ End.notebook
May 08, 2017
Ex. 1 Write an equation of a parabola with vertex at the origin and the given focus or directrix.
A.
focus (0, 2)
B.
directrix y = 5
Horizontal Parabolas (vertex at the origin)
equation:
focus:
(c, 0)
directrix:
x = −c
2
Alg II 10­2 Parabolas ­ End.notebook
May 08, 2017
Ex. 2 Write an equation of a parabola with vertex at the origin and the given focus or directrix.
A.
focus (−4, 0)
B.
directrix x = 1.5
Parabola Translations
3
Alg II 10­2 Parabolas ­ End.notebook
May 08, 2017
Ex. 3 Write an equation of a parabola with the given vertex and focus.
A.
vertex (3, 7); focus (5, 7)
B.
vertex (1, 4); focus (1, 7)
4