Let S be the sphere with centre M(2,3,−1) and radius 7 units.
(i) Write the Cartesian equation of S.
(ii) Find the coordinates of the points in which S intersects the xy–plane.
(iii) The plane z=4 cuts the sphere S in a circle. Determine the equation of this circle and hence find its centre and radius.
(iv) Calculate the exact area of the circle obtained in part (iii).