8 A curve has equation
$$y = \frac { x ^ { 2 } } { ( x - 1 ) ( x - 5 ) }$$
- Write down the equations of the three asymptotes to the curve.
- Show that the curve has no point of intersection with the line \(y = - 1\).
- Show that, if the curve intersects the line \(y = k\), then the \(x\)-coordinates of the points of intersection must satisfy the equation
$$( k - 1 ) x ^ { 2 } - 6 k x + 5 k = 0$$
- Show that, if this equation has equal roots, then
$$k ( 4 k + 5 ) = 0$$
- Hence find the coordinates of the two stationary points on the curve.