## Quick Reference

A locus in 3-dimensional space that can be represented in a Cartesian coordinate system by a polynomial equation in *x*, *y* and *z* of the second degree; that is, an equation of the form

*ax*^{2} + *by*^{2} + *cz*^{2} + 2*fyz* + 2*gzx* + 2*hxy* + 2*ux* + 2*vy* + 2*wz* + *d* = 0,

where the constants *a*, *b*, *c*, *f*, *g* and *h* are not all zero. When the equation represents a non-empty locus, it can be reduced by translation and rotation of axes to one of the following canonical forms, and hence classified:

*Subjects:*
Mathematics.

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