The points (0,6) and (0,−6) lie on a hyperbola whose transverse axis is along the y-axis and whose eccentricity is 2.
(i) Determine the values of a,b and c.
(ii) Write the standard form of the equation of the hyperbola.
(iii) Find the coordinates of the foci.
(iv) Obtain the equations of the asymptotes.
(v) Calculate the length of the latus rectum.