In Exercises 40 through 49, assume that the required extreme value is a relative extremum.

Four small towns in a rural area wish to pool their resources to build a television station. If the towns are located at the points (−5, 0), (1, 7), (9, 0), and (0, −8) on a rectangular map grid, where units are in miles, at what point S(a, b) should the station be located to minimize the sum of squares of the distances from the towns?