The centre (m,n) of a certain circle lies on the line 3m−4n=0 and the circle has radius 10. The circle also passes through the point (6,8).
(i) Show that the coordinates (m,n) satisfy (m−6)2+(n−8)2=100.
(ii) Solve the simultaneous equations obtained from the conditions above to find all possible coordinates of the centre.
(iii) For each centre obtained in part (ii), write the corresponding equation of the circle in expanded general form.