6 A parabola with equation \(y ^ { 2 } = 4 a x\), where \(a\) is a constant, is translated by the vector \(\left[ \begin{array} { l } 2
3 \end{array} \right]\) to give the curve \(C\). The curve \(C\) passes through the point (4, 7).

1. Show that \(a = 2\).
2. Find the values of \(k\) for which the line \(k y = x\) does not meet the curve \(C\).
   [0pt] [6 marks]