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: $T^2$ = S*S1. 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 ($a^2$*l, $b^2$*m). A fundamental result: the polar of either focus is the corresponding directrix (pole of focus (ae, 0) gives x = $\frac{a}{e}$). These formulas are identical in structure to those for circles and parabolas, making the T=0 framework universal across all conics.