8 A curve \(C\) has equation
$$y = \frac { x ( x - 3 ) } { x ^ { 2 } + 3 }$$
- State the equation of the asymptote of \(C\).
- The line \(y = k\) intersects the curve \(C\). Show that \(4 k ^ { 2 } - 4 k - 3 \leqslant 0\).
- Hence find the coordinates of the stationary points of the curve \(C\). (No credit will be given for solutions based on differentiation.)
\includegraphics[max width=\textwidth, alt={}, center]{e45b07a3-e303-4caf-8f3a-5341bad7560a-24_2488_1728_219_141}