# Conics Introduction

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```					Conic Sections

An Introduction
Conic Sections
• A conic section is the intersection of a
plane and a cone.

Not that kind of plane!
A plane from GEOMETRY!!!
• By changing the inclination of the plane,
you can create:
• A circle
• A parabola
• An ellipse
• A hyperbola
Conic Sections
Which conic section?
Which conic section?
Which conic section?
Which conic section?
Circles
Ellipse
Hyperbola
Conic Sections
Parabola
y  ax   2

Circle    x and y term
x2  y2  r 2

2
 2 1
Equal to 1                        a    b
Hyperbola       subtraction          2   2                y 2 x2
x    y                     2 1
Equal to 1               2 1    or        2
2
a b                   b    a
Applet
• http://www.shodor.org/interactivate/activiti
es/conics/index.html
Paper Folding
• http://www-
cm.math.uiuc.edu/~halperin/foldingpaper.h
tml
•   How To Construct An Ellipse Using Wax Paper:
•   Start out with a piece of uncrumbled wax paper about the size of half a sheet of
standard notebook paper (8.5 x 11). Draw a circle in the center of the wax paper
without writing off the paper. Then draw a point anywhere inside the circle excluding
on the circle and the center. The next step is to fold up the circle so it touches the
point inside. When this portion of the circle is aligned with the point, crease the paper
and fold it accordingly. Choose another part of the circle and align this with the point,
creasing the wax paper. Repeat this step several times until the majority of the circle
has touched the point inside or until an ellipse is visible.
•   How To Construct A Hyperbola Using Wax Paper:
•   Start out with a piece of uncrumbled wax paper about the size of half a sheet of
standard notebook paper (8.5 x 11). Draw a circle in the center of the wax paper
without writing off the paper. Then draw a point anywhere outside the circle
excluding on the circle. The next step is to fold up the point onto the circle so they
are touching. When this point is aligned onto the circle, crease the paper and fold it
accordingly. Choose another part of the circle and align this with the point, creasing
the wax paper. Repeat this step several times until the point has touched the
majority of the circle or until a hyperbola is visible.
Conic Sections diagram and info: http://www.math2.org/math/algebra/conics.htm
http://www.math.com/tables/algebra/conics.htm
tutorial: http://www.coolmath.com/algebra/Algebra2/index.html

```
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