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.
The gif animations should run on most systems and the file sizes are relatively small.
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.)
The collection of animations in gif and mov format can be downloaded; see the zipped download category at the bottom of the following table.
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.
To see an animation of the conic sections as
a plane is being rotated through a double cone go to http://www.math.odu.edu/cbii/calcanim/index.html
animation includes the three-dimensional image of the cone
with the plane, as well as the corresponding two-dimensional image of the plane itself. This excellent demo was
done in Mathcad. The authors granted us permission to use their original file as the basis for the following animation. To download this animation in both gif and mov format click here.
To see the intersections illustrated a using
Mathematica graphics go to http://www.nsm.iup.edu/ma/gsstoudt/conics/conicsmma.html
The applet at http://thorin.adnc.com/~topquark/math/conicsec.html
allows you to specify a plane in three-dimensional space.
The applet plots the intersection of the plane with a cone whose sides have unit slope. The type of figure generated is shown
At http://math2.org/math/algebra/conics.htm is a discussion of conic sections generated by intersecting a double cone with detailed descriptions of the cases including degenerate cases. Also included are very nice figures.
Gallery of Animations
Ellipses centered at (0, 0)
| Ellipses centered at
| Parabolas in the form
also an EX file
|Parabolas in the form
also an EX file
| Hyperbolas centered
at (0, 0)
| Hyperbolas centered
|Conic Sections (polar form)
Vary k: Gif Animation
Zipped downloads ==>
|Download (all) Gif and Mov Animations (large file) Download (3) Excel files|
Other Selected Resources:
A parabola (and more) java applet at http://www-groups.dcs.st-and.ac.uk/~history/Java/Parabola.html
The Standard and General Form Equations for Parabolas
Javasketchpad applet: The Conic Sections As the Locus of Perpendicular Bisectors
Nine applets for conics (fee involved) at
Translations and Rotations of Conic Sections
This applet lets you investigate the general quadratic Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
A Geometer's Sketch Pad routine for a general quadratic is available
for download by clicking here.
An Introduction To Conic Sections at http://www.krellinst.org/UCES/archive/resources/conics
with historical, geometric, and algebraic notes, as well as exercises.
Various conic contributions to the Math
Archives at http://archives.math.utk.edu/topics/precalculus.html
The Ellipse Game at http://johnbanks.maths.latrobe.edu.au/Games/Ellipse/
is an applet to provide
practice finding the foci.
Eric Weisstein's World of Mathematics
discussion of conic sections at
Special thanks to P. Bogacki and
G. Melrose of Old Dominion University for their permission to use the
animation of a plane intersecting a double cone. They kindly regenerated the animation to incorporate
the labeling of the conic sections.
The Geometer's Sketchpad routines were
constructed by Mark Yates of The McCallie School and are
used with his permission.
The Excel files were written by Xia Zhao, a student at Temple University, and David R. Hill, Temple University.
Special thanks to Deane Arganbright of University of Tennessee at Martin and to Walter Hunter at Montgomery County Community College for their assistance with the development of the Excel files that accompany this gallery. The book "Mathematical Modeling with Excel", by Erich Neuwrith and Deane Arganbright (Brooks-Cole) provides a rich source of information for developing Excel routines for mathematical instruction.
This gallery was developed by David R. Hill, Temple University.
8/6/03DRH Last updated 2/11/2005
As of 8/29/03