a conic section (though it may be degenerate), and all conic sections arise in this way. The most general equation is of the form

with all coefficients real numbers and not all zero.

Matrix notation

The above equation can be written in matrix notation as

The general equation can also be written as

This form is a specialization of the homogeneous form used in the more general setting of projective geometry (see below).

Discriminant

The conic