The Ultimate Weapon

There are $M$ enemy troops on the ground. The battleground is similar to cartesian coordinate system. Each troop is given a coordinate $(x,y)$ on this system. Joseph has the latest tech to fight these troops - a duplex railgun. It is placed at the point ($x_0$,$y_0$). It takes only a single shot to destroy all the troops situated on some line that passes through ($x_0$,$y_0$). Find the minim