For a hyperbola centred at the origin with its transverse axis along the y-axis, the length of the semi-conjugate axis is 6 units and the distance between its foci is 20 units.
a. (i) Calculate the values of b (already given), c and a.
b. (ii) Write the standard equation of the hyperbola.
c. (iii) Determine its eccentricity.
d. (iv) State the coordinates of its vertices.