How do we find the locus of points?

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

One Point:
What is the locus of points equidistant from one point?
The locus of points equidistant from a single point is a set of points equidistant from the next point in every direction.
Two Points:
What is the locus of points equidistant from two points?
The locus of points equidistant from two points is the perpendicular bisector of the line segment, connecting the two points.
One Line:
What is the locus of points equidistant from one line?
The locus of points equidistant from a line are two lines on opposite sides equidistant and are parallel in every direction.
Two Parallel Lines:
What is the locus of points equidistant from two parallel lines?
The locus of points equidistant from two parallel lines is another line half-way between both lines and parallel to each of them.
Two Intersecting Lines:
What is the locus of points equidistant from two intersecting lines?
The locus of points equidistant from two intersecting lines are two additional lines that bisect the angles formed by the original lines.