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.