A botanical garden plans to build a water pond in the shape of an ellipse with its major axis vertical. The distance between the foci is 6m and the intended length of the minor axis is 8m. The centre of the pond will coincide with the origin of a coordinate system drawn on the ground.
a. (i) Determine the lengths of the semi-major and semi-minor axes.
b. (ii) Compute the coordinates of the two foci.
c. (iii) Obtain the Cartesian equation of the boundary of the pond.