Draw a Locus

Draw a Locus

Top 

Were now going to re-create the old exercise of drawing an ellipse using a pencil, two pins, and a piece of string.

  1. Turn on the axes by clicking on the grid tool in the toolbar.

Tutorial 2 (Grid button) 

  1. Make two line segments, AB and BC. Points A and C are the pins, while B represents the pencil.

 

  1. Select point A.
  2. Add an input constraint of type Coordinate to set the coordinates of the point.
  3. When the constraint highlights, enter (not forgetting the parentheses):

(-a,0)

  1. Select point C and constrain its coordinates to be at (a,0).

 

  1. Scroll down, if necessary, to see the value of a in the Variables palette.

Tutorial 2 (value of a) 

  1. Reselect A and drag it to the right a short distance. As you drag, notice:
  • A is now constrained to lie along the X axis; moving it up or down has no effect.
  • When you move A, C also moves.
  • When you move A, the value of the associated variable a changes in the Variables list.
  1. Select the line AB and constrain its length to be distance t.
  2. Select the line BC and constrain its length to be Lt. L now represents the length of the string.

 

  1. Notice that the two new variables have appeared in the Variables list.

Tutorial 2 (value of a, L, t) 

  1. Select B.
  2. In the Construct palette, select Locus to construct a locus through B.

Locus_Construction 

  1. In the resulting dialog, choose t as the parameter to vary, and enter start and end values of 025, guesses that will probably produce a complete curve.

The locus appears half of an ellipse, above the X axis.

 

  1. Now drag B up and down, the equivalent of changing the length of the string, and seeing how the ellipse changes. You can also drag A or C to change the position of the pins.