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Conic Sections

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.

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Conic Sections

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  1. Conic Sections Colleen Beaudoin For FCIT Note: All clipart found on Clipart ETC

  2. 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.

  3. The Circle The plane that intersects the cone is perpendicular to the axis of symmetry of the cone.

  4. 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”.

  5. The Parabola The plane that intersects the cone is parallel to an element of the cone.

  6. The Hyperbola The plane that intersects the cone is parallel to the axis of symmetry of the cone.

  7. Conic Sections Classroom Activity

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Now, students in each group must create a list of conic sections they see in real life. Share with the class.

  14. Where do you see conic sections in real life?

  15. Where do you see conic sections in real life?

  16. Review What are the 4 conic sections we discussed and how are they defined?

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