Be sure to download GeoGebra Augmented Reality on your device first.
Link to GeoGebra Augmented Reality app from App Store.
1) Open up GeoGebra Augmented Reality app on iPad or iPhone.
2) Go to MENU. Select "Two Functions".
3) Delete the first equation (provided). For blue (top) equation, enter . For bottom equation, type in .
4) Take a ball (sphere) and show how this is a perfect model for such a sphere. See 0:12 - 0:15 in video.
5) Delete bottom equation (pink). Change top (blue) equation to . (See 0:30 in video). This creates a cone. If you have a funnel, you can show what you see in video from 0:44 to 0:54.
6) Enter new pink equation z = 3. This illustrates one of the four main conic section types: A CIRCLE. See 1:02 to 1:13 in video.
7) Now change pink equation to z = 2x + 1. This will create a cross section (intersection) that is a PARABOLA (2nd type of conic section). See 1:16 - 1:31 in video.
8) Now change pink equation to z = 0.5x + 3. This will create a cross section (intersection) that is an ELLIPSE (3rd type of conic section). See 1:32 to 1:44 in video.
9) Now change pink equation to z = 5x + 2. This will create a cross section (intersection) that is a HYPERBOLA (4th type of conic section). See 1:45 to END in video.