Problem

The equation of a curve is $2x^2 - kxy + 2 = 0$ and the equation of a line is $y = px + 3$, where $k$ and $p$ are constants.

(a) Given that $k = 2$ and $p = 11$, find the coordinates of the points of intersection of the curve and the line.

(b) Given instead that $p = 4$, find the set of values of $k$ for which the curve and the line do not intersect.