[wyftpnao] Parabolic and hyperbolic cones as quadric surfaces

Missing from most lists of quadrics (quadratic surfaces) are the parabolic cone (an extreme version of an oblique elliptic cone), and the hyperbolic cone (lines through hyperbola and non-coplanar point, not hyperbola revolved around an asymptote to which the name seems also sometimes applied).  Are they not quadrics?

They seem difficult to visualize.