5

5. Hyperboloid of one sheet: (a) Once again, the sliders don't go all the way to 0. Why not? Make all of them as small as possible and zoom in to see the resulting hyperboloid. What other quadric surface does the picture resemble? (b) Look at the equation. What should happen for the slices r = A or z = -A? Check this in the first picture; recall that A = 1 there. (c) Does there always have to be a "hole" through the hyperboloid, or could the sides touch at the origin? In other words, could the cross section given by z = 0 ever be a point instead of an ellipse? Experiment with the second picture; be sure to look directly from the top and zoom in before just assuming that the hole is gone