Given white points and black points (up to ten of each in this Demonstration), it is sometimes possible to find a separating line with all the white points on one side and all the black points on the other side (none of the points should lie on the line). This Demonstration shows a separating line and a separating parabola when they exist; you can drag the points.

When the points can be separated by a vertical line, it takes precedence over a separating parabola. The points are at the centers of the disks, so when a disk touches the line, the point may still be off the line.

Reference

[1] J. Matoušek and B. Gärtner, Understanding and Using Linear Programming, New York: Springer, 2007.