Conic Section Gallery

The following is a gallery of demos for illustrating selected families of conic sections These figures and animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions. Two file formats, gif and mov are available.

  1. The gif animations should run on most systems and the file sizes are relatively small. 

  2. The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.) 

  3. The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.

  4. We use abbreviations, GSP for Geometer's Sketch Pad 4, MAT for MATLAB, and EX for Excel spread sheet, to indicate the software used to generate the frames of the animation. If alternate corresponding software is also available there will be more than one abbreviation in that category. Software routines can also be downloaded.

Circles, Ellipses, Parabolas, and Hyperbolas

The conic sections are the non-degenerate curves generated by the intersections of a plane with one or two cones in the double cone as pictured below. For a plane perpendicular to the axis of the cone, a circle is produced. For a plane which is not perpendicular to the axis and which intersects only one cone, the curve produced is either an ellipse or a parabola. The curve
produced by a plane intersecting both cones is a hyperbola
.

 

Gallery of Animations

Circles

GSP

Vary r: Gif Animation   
           Mov Animation

Vary h: Gif Animation   
            Mov Animation

Vary k: Gif Animation   
            Mov Animation

 Ellipses centered at (0, 0)

GSP

 

Vary a: Gif Animation   
            Mov Animation

Vary b: Gif Animation   
            Mov Animation
 

 Ellipses centered at (h, k))

GSP
 

Vary h: Gif Animation   
            Mov Animation

Vary k: Gif Animation   
            Mov Animation

 Parabolas in the form

GSP
also an EX file

 

Vary a: Gif Animation   
            Mov Animation

Vary b: Gif Animation   
            Mov Animation

Vary c: Gif Animation   
            Mov Animation

Parabolas in the form

GSP
also an EX file

 

Vary h: Gif Animation   
            Mov Animation

Vary k: Gif Animation   
            Mov Animation
 

 Hyperbolas centered at (0, 0)

GSP

 

Vary a: Gif Animation   
            Mov Animation

Vary b: Gif Animation   
            Mov Animation
 

 Hyperbolas centered at (h,k)

GSP

 

Vary h: Gif Animation   
            Mov Animation

Vary k: Gif Animation   
            Mov Animation

Conic Sections (polar form)

EX

Vary k: Gif Animation   
            Mov Animation

Vary e: Gif Animation   
            Mov Animation

 

Zipped downloads ==>

 
 Download (all) Gif and Mov Animations (large file)

Download (1) Geometer's Sketch Pad file with 7 programs

Download (3) Excel files

 

Other Selected Resources:

Credits: 

 

 

8/6/03DRH          Last updated  2/11/2005

As of 8/29/03