A line has equation y = 2x + c and a curve has equation y = 8 − 2x − x².
i. For the case where the line is a tangent to the curve, find the value of the constant c.
ii. For the case where c = 11, find the x-coordinates of the points of intersection of the line and the curve.
Find also, by integration, the area of the region between the line and the curve.