# Circular Paraboloid of Revolution

- Author:
- Tim Brzezinski

Recall the locus definition of a

**parabola**(illustrated here if you need a refresher). Well, imagine spinning this parabola 360 degrees about its axis (of symmetry). Doing so yields a 3D solid called a**circular paraboloid of revolution.**Interact with this applet for a few minutes.*Be sure to slide the***Slide Me!**slider completely once**messing around with the other sliders!***before***Note: Point P is a point that lies on this solid. Move it wherever you'd like.**After doing so, answer the question that follows.**To explore this resource in Augmented Reality, see the directions that appear below the applet.**A circular paraboloid of revolution is a locus (set of points that satisfy a condition or set of conditions). How would you describe this locus?

## To Explore in Augmented Reality:

1) Open up GeoGebra 3D app on your device.
2) Go to MENU, OPEN. Under SEARCH, type

**g3uusvay**. 3)**The xcoord slider controls the x-coordinate of point P. The ycoord slider controls the y-coordinate of point P.****The yellow e slider controls the opacity of the paraboloid.****The blue i slider controls the opacity of the (directrix) plane.****The a slider stretches (or compresses) the paraboloid vertically (with respect to z).****The slider named d provides the animation.****Set the boolean variable****n equal to "true" if you want to see the 2d-parabola****= cross section of the paraboloid of revolution and vertical plane containing P.**