Cylinders and Quadric Surfaces
- Justin Mears
Part 1: Cylinders
z = x^2in the input line and press
enter. Try plotting the parabolic cylinder in the graph below.
Using the two examples above as references, with which axis are the straight lines parallel in the graph of the parabolic cylinder ?
Part 2: Quadric Surfaces
Hyperboloid of One Sheet
Hyperboloid of Two Sheets
1 = z^2 - x^2 - y^2and hit
enter. Geogebra understands that this is an implicitly defined surface and will draw it for you. The actual equations for these surfaces (given in your textbook) are more complicated than the examples I have given you here.
In the graph below, plot the surface given by the equation What is the resulting surface?
What surface results when ?
There are three distinct surfaces that occur as k varies between [-5,5]. What three surfaces do you see heree and for what values of k do they occur?