Conic Sections

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Conic Sections

• An Introduction

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Conic Sections

• A conic section is the intersection of a plane
  and a cone.

Not that kind of plane! A plane from GEOMETRY!!!
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• By changing the inclination of the plane, you can
  create
• A circle
• A parabola
• An ellipse
• A hyperbola

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Conic Sections
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Which conic section?
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Which conic section?
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Which conic section?
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Which conic section?
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Circles
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Ellipse
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Hyperbola
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Conic Sections
x and y term Equal to radius squared
addition Equal to 1
subtraction Equal to 1
or
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Applet

• http//www.shodor.org/interactivate/activities/con
  ics/index.html

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Paper Folding

• http//www-cm.math.uiuc.edu/halperin/foldingpaper
  .html

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• 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.

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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/Algebr
a2/index.html