Express \(4 - 10 x - x ^ { 2 }\) in the form \(p - ( x + q ) ^ { 2 }\).
Hence write down the equation of the line of symmetry of the curve with equation \(y = 4 - 10 x - x ^ { 2 }\).
The curve \(C\) has equation \(y = 4 - 10 x - x ^ { 2 }\) and the line \(L\) has equation \(y = k ( 4 x - 13 )\), where \(k\) is a constant.
Show that the \(x\)-coordinates of any points of intersection of the curve \(C\) with the line \(L\) satisfy the equation
$$x ^ { 2 } + 2 ( 2 k + 5 ) x - ( 13 k + 4 ) = 0$$
Given that the curve \(C\) and the line \(L\) intersect in two distinct points, show that
$$4 k ^ { 2 } + 33 k + 29 > 0$$
Solve the inequality \(4 k ^ { 2 } + 33 k + 29 > 0\).