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Activity 9.7.2 .
Each equation below is a cylinder surface in
\(\R^3\text{.}\) To sketch the cylinder surfaces in
\(xyz\) -space, you should first draw the generating curve in the
\(xy\) -plane,
\(xz\) -plane, or
\(yz\) -plane (depending on which two variables appear in the equation) and then then sketch a three-dimensional cylinder surface by thinking about how the rulings will run.
(a)
\(2x-y+1=0\) is called a
linear cylinder surface .
(b)
\((x-1)^2+(y+2)^2=4\) is called a
right-circular cylinder surface .
(c)
\(\frac{x^2}{9}+\frac{z^2}{4}=1\) is called an
elliptic cylinder surface .
(d)
\(x^2-y^2=1\) is called an
hyperbolic cylinder surface .