information:classification
Homogeneous coordinates

In homogeneous coordinates a conic section can be represented as:

Or in matrix notation

The 3 × 3 matrix above is called the matrix of the conic section.

Some authors prefer to write the general homogeneous equation as

(or some variation of this) so that the matrix of the conic section has the simpler form,

but this notation is not used in this article.

If the determinant of the matrix of the conic section is zero, the conic section is degenerate.

As multiplying all six coefficients by the same non-zero scalar yields an equation with the same set of zeros, one can consider conics, represented by (A, B, C, D, E, F) as points in the five-dimensional projective space P 5. {\displaystyle \mathbf {P} ^{5}.}