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In geometry, a circular section is a circle on a quadric surface. It is a special plane section of the quadric, as this circle is the intersection with the quadric of the plane containing the circle.
Any plane section of a sphere is a circular section, if it contains at least 2 points. Any quadric of revolution contains circles as sections with planes that are orthogonal to its axis; it does not contain any other circles, if it is not a sphere. More hidden are circles on other quadrics, such as tri-axial ellipsoids, elliptic cylinders, etc. Nevertheless, it is true that:
Equivalently, all quadric surfaces contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids.
If a quadric contains a circle, then every intersection of the quadric with a plane parallel to this circle is also a circle, provided it contains at least two points. Except for spheres, the circles contained in a quadric, if any, are all parallel to one of two fixed planes.