An orbital manned scientific lab is placed on an eccentric elliptical orbit described by x2+5y2+x+3y = 10, the reference system (x, y) being the center of the earth. All radio communications with the ground stations are going to be monitored via a satellite that will be fixed with respect to the reference system. The power required to communicate between the satellite and the lab is proportional to the square of the distance between the two.
Assuming that the satellite will be positioned in the plane of the ellipse, what should be the position of the satellite so that the maximum power required for transmissions between the lab and the satellite can be minimized? Formulate as a nonlinear program.