Conic Sections

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Conic Sections

• Colleen Beaudoin
• For FCIT
• Note All clipart found on Clipart ETC

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Conic Sections Figures created when a
double-napped cone is cut by a plane
Note With the exception of the hyperbola, the
plane intersects only one nappe of the cone.
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The Circle
The plane that intersects the cone is
perpendicular to the axis of symmetry of the cone.
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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.
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The Parabola
The plane that intersects the cone is parallel
to an element of the cone.
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The Hyperbola
The plane that intersects the cone is parallel to
the axis of symmetry of the cone.
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Conic Sections Classroom Activity
 
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Conic Sections Classroom Activity

• 1. Put students into groups and give each group
• 4 cone-shaped paper cups (or party hats)
• 4 sheets of paper
•  paint on a paper plate

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Conic Sections Classroom Activity

• 2. Each group should cut the first cone flat
  across the bottom as if a plane intersected it
  perpendicular to its axis. Then, dip the cone
  into the paint and stamp the paper to see the
  outline of where the cone was cut. Have each
  group write down the name of the shape they see
  on their paper.

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Conic Sections Classroom Activity

• 3. Cut the second cone as if a plane is
  intersecting it neither parallel nor
  perpendicular to the axis.  Be sure to cut all
  the way through the cone (hitting all sides).
  Dip the edge in paint and stamp the paper. Label
  the shape produced. 
• Have students compare and contrast the two
  shapes they have on their paper.
•  

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Conic Sections Classroom Activity

• 4. Have students cut the third cone as if a plane
  is passing through it parallel to the slant of
  the outside edge.  Again, dip the cut edge in the
  paint and stamp the paper. Label the shape.
•  

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Conic Sections Classroom Activity

• 5. With the fourth cone, cut the cone as if a
  plane was passing through it parallel to the axis
  of symmetry. Dip the cut edge in the paint and
  stamp the paper. Label the shape.
•  

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Now, students in each group must create a list of
conic sections they see in real life. Share
with the class.
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Where do you see conic sections in real life?
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Where do you see conic sections in real life?
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Review

• What are the 4 conic sections we discussed and
  how are they defined?