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Active Calculus - Multivariable

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.