An elementary treatise on cubic and quartic curves, by A. B. Basset.

IMAGINARY SINGULARITIES. 29
and the resulting equation will represent a curve having a pair of
imaginary singularities of the proposed kind on the line
Ax + By C= O.
When the imaginary singularities are at infinity, we must
proceed as before, but write I for a, where I= 0 is the line at
infinity.
The most interesting case of imaginary singularities at infinity
occurs when the singularities are situated at the circular points at
infinity; but the discussion of this question must be postponed to
a subsequent chapter. We shall merely observe that the Cartesian
equation of a curve having a pair of singularities at these points
may be obtained by first writing down the trilinear equation of a
curve which has the proposed singularities at B and C, and then
writing
a = const., 3=x + y, y = x - Ly.