Chapter 3: Functions of Several Variables
Section 3.3: Quadric Surfaces
Example 3.3.13
Give an equation for the elliptic cylinder whose central axis is the line through 1,2,3, parallel to the y-axis. The cross sections perpendicular to the central axis should be ellipses with a vertical semi-major axis of length 3 and a horizontal semi-minor axis of length 1. Graph this cylinder for y∈1,5.
Solution
An equation for the requisite elliptic cylinder is
x−12+z−3232=1
A graph of this cylinder can be seen in Figure 3.3.13(a).
(The code for drawing the graph of the cylinder is hidden input for the cell in which the figure sits.)
use plots in module() local q,p1,p2,p3; q:=9*x^2+z^2-18*x-6*z+9; p1:=plots:-implicitplot3d(9*x^2+z^2-18*x-6*z+9=0,x=0..2,y=1..5,z=0..6, style=surface,grid=[25,25,25]); p2:=spacecurve([[1,0,3],[1,6,3]],color=red,thickness=3,numpoints=2); p3:=display(p1,p2,scaling=constrained,axes=frame,view=[0..2,0..6,0..6], tickmarks=[3,6,6],orientation=[-35,70,0]); print(p3); end module: end use:
Figure 3.3.13(a) Elliptic cylinder
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