5th of March, 2012: How do we find the locus of points?

The locus is the set of all points that satisfy a given condition. It is a general graph of a given equation.

There are five locus theorems:

1. One point: A circle with the original point at its center.
2. Two fixed points: The locus of points equidistant from two points is the perpendicular bisector of the line segment connecting the two points
3. One line: the locus of points equidistant from a line are two lines, on opposite sides, and equidistant and parallel to that line
4. Two parallel lines: A line through the middle of the two lines
5. Two intersecting lines: Two intersecting lines half-way between the two original points