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