8. A parabola has equation \(y ^ { 2 } = 4 a x , a > 0\). The point \(Q \left( a q ^ { 2 } , 2 a q \right)\) lies on the parabola.
- Show that an equation of the tangent to the parabola at \(Q\) is
$$y q = x + a q ^ { 2 }$$
This tangent meets the \(y\)-axis at the point \(R\).
- Find an equation of the line \(l\) which passes through \(R\) and is perpendicular to the tangent at \(Q\).
- Show that \(l\) passes through the focus of the parabola.
- Find the coordinates of the point where \(I\) meets the directrix of the parabola.