In this video, we are going to look at compound loci. This is very similar to a regular locus, except now there are two or more conditions that have to be met.

For example:
Given line $K$ and a point on the line, point $P$, find the compound loci of points that are 4 inches from point $P$, and also 2 inches from line $K$.

First, let’s look at one condition at a time, and then decide which points can satisfy both of them. So, the locus of points that are 4 inches from point $P$ will be a circle with the center located at point $P$ with a radius of 4 inches.

The locus of points 2 inches from line $K$ will be two parallel lines above and below line $K$ located exactly 2 inches from it.

We are looking for points that satisfy both conditions. Four different points can satisfy both conditions. These points are the points on the locus of point $P$ (a circle) at which the locus of line $K$ (two parallel lines) intersects the circle.