8. The points \(P \left( 4 k ^ { 2 } , 8 k \right)\) and \(Q \left( k ^ { 2 } , 4 k \right)\), where \(k\) is a constant, lie on the parabola \(C\) with equation \(y ^ { 2 } = 16 x\).
The straight line \(l _ { 1 }\) passes through the points \(P\) and \(Q\).
- Show that an equation of the line \(l _ { 1 }\) is given by
$$3 k y - 4 x = 8 k ^ { 2 }$$
The line \(l _ { 2 }\) is perpendicular to the line \(l _ { 1 }\) and passes through the focus of the parabola \(C\). The line \(l _ { 2 }\) meets the directrix of \(C\) at the point \(R\).
- Find, in terms of \(k\), the \(y\) coordinate of the point \(R\).