A parabola is defined as the collection of all points P in the plane that are the same distance from a fixed point F as they are from a fixed line D. The point F is called the focus of the parabola, and the line D is its directrix. As a result, a

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A parabola is defined as the collection of all
points P in the plane that are the same distance
from a fixed point F as they are from a fixed
line D. The point F is called the focus of the
parabola, and the line D is its directrix. As a
result, a parabola is the set of points P for
which
d(F, P) d(P, D)
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(No Transcript)
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y
D x -a
V
x
F (a, 0)
4
y
D x a
V
x
F (-a, 0)
5
y
F (0, a)
x
V
D y -a
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y
D y a
x
F (0, -a)
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Find an equation of the parabola with vertex at
the origin and focus (-2, 0). Graph the equation
by hand and using a graphing utility.
Vertex (0, 0) Focus (-2, 0) (-a, 0)
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The line segment joining the two points above and
below the focus is called the latus rectum.
Let x -2 (the x-coordinate of the focus)
The points defining the latus rectum are (-2, -4)
and (-2, 4).
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(-2, 4)
(0, 0)
(-2, -4)
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Parabola with Axis of Symmetry Parallel to
x-Axis, Opens to the Right, a gt 0.
D x -a h
y
V (h, k)
Axis of symmetryy k
F (h a, k)
x
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Parabola with Axis of Symmetry Parallel to
x-Axis, Opens to the Left, a gt 0.
D x a h
y
Axis of symmetry y k
F (h - a, k)
x
V (h, k)
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Parabola with Axis of Symmetry Parallel to
y-Axis, Opens up, a gt 0.
Axis of symmetry x h
y
F (h, k a)
V (h, k)
D y - a k
x
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Parabola with Axis of Symmetry Parallel to
y-Axis, Opens down, a gt 0.
Axis of symmetry x h
y
D y a k
V (h, k)
F (h, k - a)
x
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Find the vertex, focus and
directrix of
Graph the
parabola by hand
and using a graphing utility.
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Vertex (h, k) (-2, -3)
a 2
Focus (-2, -3 2) (-2, -1)
Directrix y -a k -2 -3 -5
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Latus Rectum Let y -1
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(-6, -1)
(2, -1)
y -5
(-2, -3)
(-2, -1)