

A line through the focus and a line perpendicular to the directrix make the same angle with the tangent.



Given a point (the focus) and a line (the directrix), a parabola can be defined as the locus of the points whose distance from the focus is equal to t...



We take the parabola, whose vertex is (0,0) and whose focus is (0,a). The point at parametric location t is (2*a*t,a*t^2).



Take two tangents of a parabola that are perpendicular to each other. The locus of all such points will be a line. This line is the directrix.



The slope of the tangent at parametric location t gives a further characterization:



This is the directrix.



Take two nonparallel tangents of a parabola, and the angle at their intersection can be calculated.



We look at the caustic of the parabola y=x^2 formed by a set of rays at angle θ to the xaxis.



