For a parabola y^2 = 4ax:
1. Find the equation of the tangent at P ( at^2, 2at ) on the parabola.
2. Find the point Q on the parabola so that PQ passes through the focus F ( a, 0 ) of the parabola
3. Show that the tangents at P and Q intersect on the directrix of the parabola
This is a problem regarding tangent and focus of a parabola.