## Conics from a Traditional Standpoint

 Conic Sections     This page presents information about the traditional views of conic sections.    Conics from a Function Viewpoint are presented on another page.

 Think Two Cones     The name conic refers to the cones. Think really, really, thin, infinitly big, empty ice cream cone -- just the shell, just one-point-thick.     Think thinner than a piece of paper.     Think the light blue is the outer surface of the cone one-point-thick.     Think the dark blue is the inner surface of the cone one-point-thick. Remember that a point has no thickness, so, this is really thin.     The cones are sliced or cut by a plane to create a section or part of the cone. See below.     Though cuts are drawn to show an area, remember that the cut is really only the edge -- the part of the one-point-thick empty infinite cone.     The conic section is ONLY THE BLACK STRING OF POINTS AT THE EDGE OF THE PINK SURFACE.

Individual Pictures

Conic Sections
 circle ellipse parabola hyperbola
Degenerate Conic Sections
 point line 2 intersecting lines

 All Conic Sections     Conic section are ancient mathematical ideas. They are curves, strings of points.     To a mathematician, a curve might be straight, as in a line, or have a bend or two as in a parabola or hyperbola.     It might be closed or form a loop, as in a circle or ellipse.     A point, a line, or two intersecting lines are often called degenerate conics because they are possible to form as a plane cuts the cones, but, are not the circle, ellipse, parabola, or hyperbola usually listed as the conices. Conic Sections circle ellipse parabola hyperbola Degenerate Conic Sections point line 2 intersecting lines

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 Cut the Cones Perspective     Return to the Individual Pictures shown above and click on each picture so you are better able to examine how a plane passing through one or more cones creates the black string of points called a conic.     Examine the pictures and contemplate the angle at which the plane cuts the cones.     Examine the picture and summary below for a complete analysis.

 Eccentricity Perspective Conic Sections circle ellipse parabola hyperbola Degenerate Conic Sections point line 2 intersecting lines

 Functions Perspective     Visit Conics from A Functions, modern, calculator useful, basis.