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Conic Sections

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

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.

The Circle

The plane that intersects the cone is

perpendicular to the axis of symmetry of the cone.

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.

The Parabola

The plane that intersects the cone is parallel

to an element of the cone.

The Hyperbola

The plane that intersects the cone is parallel to

the axis of symmetry of the cone.

Conic Sections Classroom Activity

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

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.

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.

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.

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.

Now, students in each group must create a list of

conic sections they see in real life. Share

with the class.

Where do you see conic sections in real life?

Where do you see conic sections in real life?

Review

- What are the 4 conic sections we discussed and

how are they defined?

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