Download - Analytic Geometry
Parabolas, hyperbolas, ellipses,
circles
Analytic GeometryConic 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?
Dimensionsa 0 b
y
x
y
x
z
1D
2D
3D
Ordered Pairs Review : (a,b)
b
a
I (a,b)II(-a,b)
IV (a,-b)III(-a,-b)
Finding the inclination of a line
Horizontal Vertical Acute Obtuse
Θ=0
Θ=∏/2
Θ Θ
Example: make sure you are in radian
modeFind the inclination of the line 2x+3y = 6
m= -2/3m= -a/b
Θ Θ = ∏ + arctan (-2/3)
Θ = ∏ +(-.588)
Θ = 2.554