2. Note: With the exception of the hyperbola,
the plane intersects only one nappe of the
cone.
3. The plane that intersects the cone is
perpendicular to the axis of symmetry
of the cone.
4. The plane that intersects the cone is neither
parallel nor perpendicular to the axis of
symmetry of the cone and cuts through 2
“sides”.
5. The plane that intersects the cone is
parallel to an element of the cone.
6. The plane that intersects the cone is
parallel to the axis of symmetry of the
cone.
7.
8. 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
9. 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.
10. 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.
11. 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.
12. 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.
13.
14.
15.
16. What are the 4 conic sections we discussed
and how are they defined?
