The diagram shows part of a curve, passing through the points (2, 3.5) and (5, 1.4). The gradient of the curve at any point (x, y) is -a/x^3, where a is a positive constant.
(i) Show that a = 20 and obtain the equation of the curve.
The diagram also shows lines perpendicular to the x-axis at x = 2, x = p and x = 5. Given that the areas of the regions A and B are equal,
(ii) find the value of p.