Question: How do we find compound loci?

Answer: Ok so we already know what loci is, now what is a compound loci?
Well a compound locus problem involves two or more locus conditions in one problem. The way to differentiate a compound locus problem from a regular locus problem is by the words "AND" and "AND ALSO."

Example Problem:
A treasure is buried in your backyard.  The picture below shows your backyard which contains a stump, a teepee, and a tree.  The teepee is 8 feet from the stump and 18 feet from the tree.  The treasure is equidistant from the teepee and the tree AND ALSO 6 feet from the stump.  Locate all possible points of the buried treasure. (Figure 1)

Figure 1

Step 1:
Ok first read the problem and determine ONE of the locus conditions.
Step 2:
Solve the first locus solution and plot it.
Step 3:
Re-read the problem and identify the second locus condition.
Step 4:
Solve the second locus solution and plot it.

Ok so now lets see this would look like: (Figure 2)

Figure 2

Explanation of Solutions:
The red line represents the locus which is equidistant from the teepee and the tree (the perpendicular bisector of the segment AKA the first locus condition). The blue circle represents the locus which is 6 feet from the stump (the second locus condition). These two loci intersect in two locations. The treasure could be buried at either "X" location. 

NOW YOU TRY! :D


Two points A and B are 6 units apart.  How many points are there that are equidistant from both A and B and also 5 units from A?

1. 1
2. 2
3. 3
4. 4