A quadric in space is the set of solutions of an equation of the form f(x,y,z)=0 in three variables. For regular quadrics, this equation is after suitable transformations of the following form with a,b,c>0:

ax2+by2+cz2-1=0	ellipsoids	models 1-5,12-14,42
ax2+by2-cz2-1=0	one-sheet hyperboloids	models 15,16,24,25,27,388,389
ax2-by2-cz2-1=0	two-sheet hyperboloids	models 17,26
ax2+by2-z2=0	elliptic paraboloids	models 9,19-21
ax2-by2-z2=0	hyperbolic paraboloids	models 8,10,22,23,390,391