Conic Sections

 

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Conic Sections

Conic Sections started out as a Geometric Concept.  Start with a right circular cone from Geometry.  Create a "double cone" as shown below, and "slice" the cone four ways.  ("Slicing" is the intersection of a cone and a plane.)

doublecone.jpg (6861 bytes)

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The intersection of a cone and a plane parallel to the circular base is a circle.

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The intersection of a cone and a plane not parallel to the circular base but intersects both sides of the cone is an ellipse.

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The intersection of a cone and a plane not parallel to the circular base that intersects one side of the cone is an parabola.

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The intersection of a cone and a plane perpendicular to the circular base creates the branches of a hyperbola.

cone1.jpg (9838 bytes) cone2.jpg (8264 bytes)
 

cone_circle.jpg (6891 bytes)

Circle

 

 

cone_ellipse.jpg (6186 bytes)

Ellipse

 

 

cone_parabola.jpg (9723 bytes)

Parabola

 

cone_hyperbola.jpg (8186 bytes)

Hyperbola

 

Flashlight Conic Sections

The light emitted from a flashlight with a circular lens is projected as a cone from the light bulb.  You can create Flashlight Conic Sections by projecting the light at the wall, allowing the wall to be the plane and the light from the flashlight being the cone.  Try the following shapes:

flashlight_circle.jpg (7293 bytes)

Flashlight Circle

flashlight_ellipse.jpg (6328 bytes)

Flashlight Ellipse

 

flashlight_parabola.jpg (10686 bytes)

Flashlight Parabola

 

flashlight_hyperbola.jpg (9915 bytes)

Flashlight Hyperbola

 

 

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