Transcript 49. INTRODUCTION TO ANALYTIC GEOMETRY

Analytic Geometry
Conic Sections
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
The Circle
The plane that intersects the cone is perpendicular
to the axis of symmetry of the cone.
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”
The Parabola
The plane that intersects the cone is
parallel to an element of the cone.
The Hyperbola
The plane that intersects the cone is parallel
to the axis of symmetry of the cone.
Where do you see conics
in real life?
Dimensions
a
1D
0
b
y
x
2D
z
3D
y
x
Ordered Pairs Review : (a,b)
b
(-a,b)
II
I
(a,b)
a
(-a,-b)
III
IV
(a,-b)
Finding the inclination of
a line
Θ=0
Θ
Θ
Θ=∏/2
Horizontal
Vertical
Acute
Obtuse
Example: make sure you
are in radian mode
Find the inclination of the line 2x+3y = 6
m= -a/b
m= -2/3
Θ
Θ = ∏ + arctan (-2/3)
Θ = ∏ +(-.588)
Θ = 2.554