Editing Hyperboloid (section)

===Generalised equations===
More generally, an arbitrarily oriented hyperboloid, centered at {{math|'''v'''}}, is defined by the equation
<math display="block">(\mathbf{x}-\mathbf{v})^\mathrm{T} A (\mathbf{x}-\mathbf{v}) = 1,</math>
where {{math|''A''}} is a [[matrix (mathematics)|matrix]] and {{math|'''x'''}}, {{math|'''v'''}} are [[euclidean vector|vectors]].

The [[eigenvector]]s of {{math|''A''}} define the principal directions of the hyperboloid and the [[eigenvalue]]s of A are the [[Multiplicative inverse|reciprocal]]s of the squares of the semi-axes: <math>{1/a^2}</math>, <math>{1/b^2} </math> and <math>{1/c^2}</math>. The one-sheet hyperboloid has two positive eigenvalues and one negative eigenvalue. The two-sheet hyperboloid has one positive eigenvalue and two negative eigenvalues.