Three tangent forms: point form yy1=2a(x+x1), slope form y=mx+a/m, parametric ty=x+$at^2$. The slope form shows that tangent with slope m exists for every m except 0 (no horizontal tangent to $y^2$=4ax). The tangency condition for y=mx+c is c=$\frac{a}{m}$. The point of tangency for slope m is (a/$m^2$, 2a/m). Key properties: tangents at focal chord endpoints are perpendicular and meet on the directrix. The foot of perpendicular from focus to any tangent lies on the tangent at vertex (x=0). The tangent at any point bisects the angle between the focal radius and the line perpendicular to the directrix (reflection property). The locus of intersection of perpendicular tangents is the directrix x=-a (the director curve). The sub-tangent at any point equals 2x (the x-coordinate doubled), while the sub-normal is constant at 2a.