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View Full DocumentSection 8.1 – Parabolas
1
Section 8.1
Parabolas
We previously studied parabolas as the graphs of quadratic functions.
Now we will look
at them as conic sections.
There are a few differences.
For example, when we studied
quadratic functions, we saw that the graphs of the functions could open up or down.
As
we look at conic sections, we’ll see that the graphs of these second degree equations can
also open left or right.
So, not every parabola we’ll look at in this section will be a
function.
A
parabola
is the set of all points equally distant from a fixed line and a fixed point not
on the line.
The fixed line is called the
directrix
.
The fixed point is called the
focus
.
The axis, or
axis of symmetry
, runs through the focus and is perpendicular to the
directrix.
The
vertex
is the point halfway between the focus and the directrix.
Basic “Vertical” Parabola:
Equation:
2
4
x
py
=
Focus: (0, )
p
Directrix:
y
p
= 
Focal Width:
4
p
Coordinates of Focal Chord:
(
±
2p, p)
Basic “Horizontal” Parabola
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 Fall '08
 Staff
 Conic Sections, Conic section, focal width

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