Quadrics are very interesting. To visualize some of your equations, you should use surf. It works smoothly and allows you to create animations as well as static images. A fellow student has created a web page with some nice gifs.
I am not too familiar with surf, but I have created some files which allow you to draw a paraboloid and a torus. Look for them in my surf directory. The .avi movie you can see there was my first try, but I like it.