Let y2=4ax(a>0) be a parabola opening to the right. A region R is bounded by the parabola, the straight line x=4a, and the x-axis.
a. (i) Find the coordinates of all points where the boundaries of R meet.
b. (ii) Express the area of R as a definite integral (or sum of definite integrals) with respect to a single variable.
c. (iii) Evaluate the integral(s) obtained in part (ii) and hence determine the exact area of the region R.