A curve has equation y = 5 − 2x + x² and a line has equation y = 2x + k, where k is a constant.

a. Show that the x-coordinates of the points of intersection of the curve and the line are given by the equation x² − 4x +(5 − k) = 0.    

b. For one value of k, the line intersects the curve at two distinct points, A and B, where the coordinates of A are (−2, 13). Find the coordinates of B.

c. For the case where the line is a tangent to the curve at a point C, find the value of k and the coordinates of C.