The parametric form x = x1 + rcos(theta), y = y1 + rsin(theta) expresses points on a line through (x1, y1) making angle theta with the x-axis. Here r is the signed distance from (x1, y1). This form is powerful for problems asking "find a point on the line at distance d from a given point" — just substitute r = d or r = -d. Also written as (x - x1)/cos(theta) = (y - y1)/sin(theta) = r.