THis is a presentation about analytic geometry

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