Conics Introduction

							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
          Equal to radius squared
                                             x2  y2  r 2

Ellipse    addition                          x2 y 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