Working with locus problems usually involves describing the locus (most often with a construction) AND giving reasons or proof for your description. Things are usually simplified greatly by providing a visual display to interpret the verbal statement of the problem. In the first five problems below, a visual display is provided. You may want to provide your own. The proof or reasons are needed to verify any hypothesis you generate from the visual display.
In Problem 6, interpretation by creating a visual display will help to interpret the problem and help with the reasons or proof.
See Conchoid of Nicomedes for a different sort of locus problem.
1. What is the locus of the vertices of the right angles of right triangles constructed on a fixed hypotenuse? Proof?
2. What is the locus of a points equally distant from the sides of an angle? Proof?
3. What is the locus of the centers of circles passing through two given points?
4. Given AB perpendicular to BC. D moves along AB and E moves along BC. DE is of a constant length.
What is the locus of the midpoint of DE?
What is the locus of a point on DE one-fourth the distance from D to E?
What is the locus of a point on DE three-fourths the distance from D to E?
What is the locus of a point on DE that is five-fourths the distance from E to D?
5. What is the locus of the centers of circles that are tangent to a given line at a given point?
6. What is the locus of centers of circles that have a radius r and are tangent externally to a given circle?