Now, go to the following website to generate your own conic sections. Use your own paper or go to your notes to record what you observe.

Conic Section Explorer

You can adjust the cone parameters to make the cone larger or smaller. About 1.3 to 1.5 is a good size. You can also adjust the slant of the generator line to make the cone wider or narrower. If you want the cone back to its original size and shape, just reset the parameters. I would suggest that you enlarge the grid so that you can see more of the intersection.

Clicking on the cone itself allows you to rotate the figure so that you can view the intersection from a variety of angles.

You also have control over the slope of the intersecting plane as well as control over where the plane intersects the axis of symmetry. Again, if you want everything back to the original settings, just reset the parameters.

This time is “play time.” Keep the slope the same as that of the generator line. What conic section is formed? Change the “b” value and see what effect that has on the conic section by watching the graph. What happens when the plane goes through the vertex of the cone?

Make the slope steeper than the generator line. What conic section is formed? Again, change the “b” value to see how the figure changes. What happens when the plane contains the vertex?

Make the slope less steep than the generator line. What conic section is formed this time? What happens to the figure as you change the “b” value? What happens when the plane contains the vertex?