# Locus Sum of Distances

- Author:
- Melanie Palma

- Topic:
- Ellipse

1. Find as many points as you can whose SUM of its distances to F1 and F2 is _____.
- Enter the sum you are using (start with 8 or 10)
- Use the POINT tool to plot points you think fit this sum.
- Use the ARROW tool to move points and to click on boxes.
- Click on SHOW DISTANCES to see distances from points to F1 and F2.
- Use the "undo" button in the upper right corner, if you make a mistake.
- Use the "refresh" button in the upper right corner if you want to start over.
2. Once you think you have as many points as you can find, click on SHOW ME to see the shape formed by these points.
3. Try dragging F2 to change the distance between the foci. How does this affect the shape?
Which sums and focal distances give you integer coefficients in the equation?
4. Try it again with different sums.