Quadric Surfaces

It is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given plane curve.

• cone

• cylinder

• sphere

• paraboloid

It is made up of infinitely many shifted copies of the same parabola.

• parabolic cylinder

• parabolic cone

• parabolic sphere

• paraboloid

It is the graph of a second-degree equation in three variables x, y, and z.

• linear surface

• quadric surface

• quadratic surface

• cubic surface

These are the counterparts in three dimensions of the conic sections in the plane.

• quadric surfaces

• linear surfaces

• cubic surfaces

• quadratic surfaces

It is a quadric surface with elliptical and parabolic traces.

• quadric paraboloid

• quadric hyperboloid

• elliptic hyperboloid

• elliptic paraboloid

These are obtained by rotating a parabola about its axis, are used to collect and reflect light, sound, and radio and television signals.

• circular paraboloids

• elliptic paraboloids

• hyperboloids

• spheres

The same principle applies to microphones and satellite dishes in the shape of paraboloids.

• True

• False

Cooling towers for nuclear reactors are usually designed in the shape of hyperboloids of one sheet for reasons of structural stability.

• True

• False

Pairs of these are used to transmit rotational motion between skew axes.

• circular paraboloids

• elliptic parabolids

• hyperboloids

• spheres

A surface of revolution is a surface which can be generated by rotating a particular curve about a particular coordinate axis.

• True

• False