Construction of an ellipse

Let c and d be given circles centered at A. Let f be a line through A. We construct an ellipse from the triple (c,d,e). Let g be the line through A perpendicular to f. For each ray h through A, let F(h) and G(h) be the intersection points of h with c and d, respectively. Let j(h) be the line parallel to g though G(h) and i(h) be the line parallel to f through F(h). Then the locus loc1 of I(h) is an ellipse.