Maple #2 is due Thursday 20 Jan 2000

For FULL credit STAPLE your sheets together.
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You are to plot the five functions below. Each plot must be rotated to 
a "nice" position and "look good (smooth)" . Each plot must have include
axes and the title must include your name and what was plotted. Note
that the expressions below are not necessarily in a form that Maple
likes. Be sure to answer the questions in #1 and #4.

1. Plot f(x,y) = x y again but with the implicitplot3d command.
(For the domain use -L < x, y AND z < L for interesting value of L) 
How does this differ from the plot3d version?
(Patch with contours is a good style to start with.)
2. Implicitplot3d  of a Hyperboloid of one sheet for an interesting
domain of the form -L < x, y, z < L
3. Implicitplot3d  of a Hyperboloid of two sheets for an interesting
domain of the form -L < x, y, z < L
4. According to your instructor the equation 
x^2 + x y + 2 y^2 + 7 y z - z^2 + 3 x - x z = 1
must be one of the graphs discussed
in class. Implicitplot3d the graph for a domain -L < x, y, z < L
for an L so that you can identify the graph. Identify the graph. (Carefully
inspect the graph.)
5. Combine an (nice) implicitplot of the cone z^2=x^2+y^2 with a plot3d
plot of the plane z = y - 2 with the spacecurve plot of 
their intersection x = t; y = 1-t^2/4; z=-1-t^2/4. While you are
at it, use solve({cone,plane,x=t},{x,y,z}); to obtain this space curve.