Modifying a Torus (Multiple VS) in GeoGebra Augmented Reality

Here, we explore various ways of modifying the equation of a torus to get some interesting-looking surfaces. [br][br][br]In the first screencast (V1), for which point (x,y) in the coordinate plane (i.e. in the plane z = 0) does the blue surface attain maximum value? How can we mathematically show this is true? [br][br]Enjoy!
V1
V2
V3
V4
V5
V6: Special T/Y to Mathieu Blossier (who helped me with these surface EQ's)
V7
V8

Information: Modifying a Torus (Multiple VS) in GeoGebra Augmented Reality