The parametric representation P(t)=($at^2$, 2at) for $y^2$=4ax is the single most important technique. Every formula simplifies in parametric form: tangent at t is ty=x+$at^2$ $\frac{slope 1}{t}$, normal is y+tx=2at+$at^3$ (slope -t), chord joining t1 and t2 has slope $\frac{2}{t1+t2}$. The tangent intersection point is (at1t2, a(t1+t2)) — product for x, sum for y. The focal chord condition t1t2=-1 yields the other endpoint as (-1/t). The normal re-intersection parameter is t'=-t-2/t. Three co-normal points from an external point satisfy t1+t2+t3=0 (sum of parameters is zero). These parametric results eliminate the need for coordinate geometry calculations involving square roots. The parameter t is the slope of the line from origin to the midpoint of the ordinate, providing geometric intuition for its value.