A cylindric section is the intersection of a plane with a right circular cylinder. It is a circle (if the plane is at a right angle to the axis), an ellipse, or, if the plane is parallel to the axis, a single line (if the plane is tangent to the cylinder), pair of parallel lines bounding an infinite rectangle (if the plane cuts the cylinder), or no intersection at all (if the plane misses the cylinder entirely; Hilbert and Cohn-Vossen 1999, pp. 7-8).

Hilbert, D. and Cohn-Vossen, S. "The Cylinder, the Cone, the Conic Sections, and Their Surfaces of Revolution." §2 in Geometry and the Imagination. New York: Chelsea, pp. 7-11, 1999.

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Weisstein, Eric W. "Cylindric Section." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CylindricSection.html