Now, the question I want to ask relates to finding asymptotes of curves when the point(s) at infinity are complex, as in both x & y are complex numbers. The procedure I understand for fiding the equation of the asymptote of a curve $F(x,y) = 0$ when the point at infinity is real is as follows:
1. Homogenezie the equation $F(x, y) = 0$ by substiting $x = X/W$ and $y = Y/W$; simplify the expression
2. Find points at infinity by setting W = 0 and solving the equation for Y; let's say one of the points at infinity have the homogenous coordinates of [a, b, 0]