The T = 0 substitution unifies several formulas. Chord of contact from (x1, y1): xx1/a^2 + yy1/b^2 = 1 (same as tangent form). Chord with midpoint (x1, y1): T = S1, giving xx1/a^2 + yy1/b^2 = x1^2/a^2 + y1^2/b^2. Pair of tangents from external point: T^2 = SS1. The polar of point (x1, y1) is xx1/a^2 + yy1/b^2 = 1, and if this line is lx + my = 1, the pole is (a^2l, b^2*m). A fundamental result: the polar of either focus is the corresponding directrix (pole of focus (ae, 0) gives x = a/e). These formulas are identical in structure to those for circles and parabolas, making the T=0 framework universal across all conics.