6 A curve has equation \(y = x ^ { 2 } - x + 3\) and a line has equation \(y = 3 x + a\), where \(a\) is a constant.
- Show that the \(x\)-coordinates of the points of intersection of the line and the curve are given by the equation \(x ^ { 2 } - 4 x + ( 3 - a ) = 0\).
- For the case where the line intersects the curve at two points, it is given that the \(x\)-coordinate of one of the points of intersection is - 1 . Find the \(x\)-coordinate of the other point of intersection.
- For the case where the line is a tangent to the curve at a point \(P\), find the value of \(a\) and the coordinates of \(P\).