1. Ch. 9
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

2. 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.

3. 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.)

4. HYPERBOLA:
Keep tilting so that the plane is now slicing though both the top and bottom parts of the cone.

6. 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.

7. 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. (h, k)
________
The line passing through the focus and the vertex.

8. Standard form P _______ P _____ Vertex: ___________ Focus: ___________
If the axis is _____________________ (x is squared):
Standard form
of the equation of a parabola
with vertex at (h, k) F V F V
p is the ____________________(can be positive or negative) from the vertex to the focus
Note: p≠0
P _______
P _____
Vertex: ___________
Focus: ___________
Axis of Symmetry: ________
Directrix: __________

9. Axis of Symmetry: _________
Standard form
of the equation of a parabola
with vertex at (h, k)
If the axis is ________________ __________(y is squared) F V
p is the directed distance (can be positive or negative) from the vertex to the focus
Note: p≠0 F V
P _____
P _____
Vertex: ___________
Focus: ___________
Axis of Symmetry: _________
Directrix: _________

10. **Determine Characteristics and sketch graphs**
Given the equation of a parabola, identify its
a. Vertex
b. Focus
c. Axis of symmetry
Directrix
Hint: Determine orientation of the parabola and p first.
Ex. 1)

11. **Determine Characteristics and sketch graphs**
Given the equation of a parabola, identify its
a. Vertex
b. Focus
c. Axis of symmetry
Directrix
Hint: Determine orientation of the parabola and p first.
Ex. 2)

12. HW :
For each parabolic equation, identify (and sketch) the parabola’s :
a) Vertex b) Focus c) Axis of symmetry d) Directrix.