Objective: Understand and identify basic
characteristics of conics.
Conic section (conic):
What you get (the intersection)when you cross a
plane and a double-napped cone.
4 Basic Conics:
Vertex
Axis
ELLIPSE:
The plane is slightly tilted so it’s no
longer perpendicular to the axis.
CIRCLE:
The plane is exactly perpendicular
to the cone’s axis.
PARABOLA:
Keep tilting so that the plane is
now exactly parallel to the side
of the top cone.
(Parabola occurs because one
side of the ellipse sort of falls
off.)
HYPERBOLA:
Keep tilting so that the plane is
now slicing though both the top
and bottom parts of the cone.
CONICS (Pre/Calc Style):
Conic: A __________________of points
satisfying a certain geometric property.
Ex: A circle is the locus of all points
equidistant from a fixed center point.
9.1 Parabolas
Parabola
(Conical
Definition):
________
________
The set of all points (x, y) in a plane that are __________ from a fixed line,
the _______ (parallel to the x or y-axis), and a fixed point (not on the line),
called the _________.
The midpoint between the focus and the directrix.
The line passing through the focus and the vertex.
(h, k)
Standard form
If the axis is _____________________ (x is squared):
of the equation of a parabola
with vertex at (h, k)
p is the
____________________
(can be positive or
negative) from the
vertex to the focus
Note: p≠0
V
F
F
V
P _______
P _____
Vertex: ___________
Focus: ___________
Axis of Symmetry: ________
Directrix: __________
Standard form
If the axis is ________________ __________(y is squared)
of the equation of a parabola
with vertex at (h, k)
p is the directed distance
(can be positive or
negative) from the
vertex to the focus
V
F
F
V
Note: p≠0
P _____
P _____
Vertex: ___________
Focus: ___________
Axis of Symmetry: _________
Directrix: _________
**Determine
Characteristics and
sketch graphs**
Given the equation of a
parabola, identify its
a.
b.
c.
d.
Vertex
Focus
Axis of symmetry
Directrix
Hint: Determine
orientation of the
parabola and p first.
Ex. 1)
**Determine
Characteristics and
sketch graphs**
Given the equation of a
parabola, identify its
a.
b.
c.
d.
Vertex
Focus
Axis of symmetry
Directrix
Hint: Determine
orientation of the
parabola and p first.
Ex. 2)
HW :
For each parabolic equation, identify (and sketch) the parabola’s :
a) Vertex
b) Focus
c) Axis of symmetry
d) Directrix.