The document discusses analytic geometry, which is the study of geometry using algebraic principles. It examines different types of plane intersections with cones, such as planes that are parallel, perpendicular, or neither parallel nor perpendicular to the cone's axis of symmetry. It also covers one, two, and three dimensional spaces, ordered pairs, angles including horizontal, vertical, acute and obtuse, and finding the inclination of a line using its slope-intercept form equation.

1. Parabolas
hyperbolas
ellipses
circles
ANALYTIC GEOMETRY

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

4. 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 plane that intersects the cone is
parallel to an element of the cone.

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

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. Horizontal Vertical Acute Obtuse
Θ=0
Θ=∏/2
Θ Θ

11. 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