In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a hyperboloid is a quadric

Quadric

In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in -dimensional space defined as the locus of zeros of a quadratic polynomial...

 – a type of surface in three dimension

Dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s – described by the equation
  (hyperboloid of one sheet),

or
  (hyperboloid of two sheets).

These are also called elliptical hyperboloids. If and only if a = b, it is a hyperboloid of revolution, and is also called a circular hyperboloid.
A hyperboloid of revolution of one sheet can be obtained by revolving a hyperbola around its semi-minor axis

Semi-minor axis

In geometry, the semi-minor axis is a line segment associated with most conic sections . One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis...

.