Let a=4 and b=3. A hyperbola has its centre at the origin and its transverse axis along the y–axis.
(i) Write the standard equation of the hyperbola.
(ii) Determine the coordinates of its vertices and foci.
(iii) Obtain the equations of its asymptotes.
(iv) Draw a rough sketch of the hyperbola, marking and labelling the centre, both vertices, both foci, and both asymptotes.