This page presents information about the traditional views of conic sections.

    Conics from a Function Viewpoint are presented on another page.

    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.

    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

    Click on the image to see it by itself and to print just the image using your browser.

    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.

Conic Sections
• circle
• ellipse
• parabola
• hyperbola

Degenerate Conic Sections
• point
• line
• 2 intersecting lines

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