9 The equation of a curve is \(y = \frac { 1 } { 2 } k ^ { 2 } x ^ { 2 } - 2 k x + 2\) and the equation of a line is \(y = k x + p\), where \(k\) and \(p\) are constants with \(0 < k < 1\).
- It is given that one of the points of intersection of the curve and the line has coordinates \(\left( \frac { 5 } { 2 } , \frac { 1 } { 2 } \right)\).
Find the values of \(k\) and \(p\), and find the coordinates of the other point of intersection.
\includegraphics[max width=\textwidth, alt={}, center]{39393c20-34df-4167-a8bf-e4067371de81-15_2725_35_99_20} - It is given instead that the line and the curve do not intersect.
Find the set of possible values of \(p\).