Locus Problems

Working with locus problems involves

Describing the locus

and

Giving reasons or proof for your description.

1. What is the locus of the vertex of the right angle of right triangles constructed on a fixed hypotenuse? Proof?

2. What is the locus of a point that is equally distant from the sides of an angle? Proof?

3. What is the locus of the center of circles that pass through two given points?

4. Given AB perpendicular to BC. D is on AB and E id on BC. DE is of a given 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?

7. What is the locus of the extremities of line segments meeting at a given point and bisected by a line not through the given point?

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