The document discusses conic sections and analytic geometry. It defines conic sections as shapes formed by the intersection of a plane and a cone. Specifically, it states that a circle is formed when the plane is perpendicular to the cone's axis of symmetry, an ellipse is formed when the plane is neither parallel nor perpendicular, a parabola is formed when the plane is parallel to an element of the cone, and a hyperbola is formed when the plane is parallel to the cone's axis of symmetry. It also briefly discusses dimensions, ordered pairs, finding the inclination of lines, and provides an example of finding the inclination of a line using arctan.

1. Analytic Geometry
Conic Sections

2. Analytic Geometry
Analytic geometry, usually
called coordinate geometry and
earlier referred to as Cartesian
geometry or analytical
geometry, is the study of
geometry using the principles
of algebra

3. The Circle
The plane that intersects the cone is perpendicular to
the axis of symmetry of the cone.

4. The Ellipse
The plane that intersects the cone is neither parallel
nor perpendicular to the axis of symmetry of the cone
and cuts through 2 “sides”

5. The Parabola
The plane that intersects the cone is
parallel to an element of the cone.

6. The Hyperbola
The plane that intersects the cone is parallel to the
axis of symmetry of the cone.

7. Where do you see conics
in real life?

8. Dimensions
a 0 b
y
x
y
x
z
1D
2D
3D

9. Ordered Pairs Review : (a,b)
b
a
I (a,b)
II
(-a,b)
IV (a,-b)
III
(-a,-b)

10. Finding the inclination of
a line
Horizontal Vertical Acute Obtuse
Θ=0
Θ=∏/2
Θ Θ

11. Example: make sure you
are in radian mode
Find the inclination of the line 2x+3y = 6
m= -2/3
m= -a/b
Θ Θ = ∏ + arctan (-2/3)
Θ = ∏ +(-.588)
Θ = 2.554