18 The diagram shows part of the curve with equation y = p + 10x x2, where p is a constant, and part of the line [with equation y = qx + 25, where q is a constant. The line [cuts the curve at the points A and B. The xcoordinates of A and B are 4 and 8 respectively. The line through A parallel to the x-axis intersects the curve again at the point C. a Show that p = 7 and calculate the value of q. (3 marks) b Calculate the coordinates of C. (2 marks) c The shaded region in the diagram is bounded by the curve and the line segment AC. Using integration and showing all your working, calculate the area of the shaded region. (6 marks)