Constructing a Hyperbola
Goal
Find the locus that will create a hyperbola.
A hyperbola is the set of points such that the difference of the distances from two points is constant.
Directions
1) Create a circle with center at A with defined radius d.
2) Create another circle centered at B and with radius d+a.
3) Move the slider until the circles intersect at two points. Label those two points C and D.
4) Create segments AC, AD, BC and BD.
5) Unselect the circles so that they do not show up.
6) Turn on "trace" for points C and D.
7) Move the slider around to see the points C and D "create" a hyperbola.
Observations?
Given the definition of a hyperbola (see above) why did we construct the circles in this way? Hint: How did we define our radii?
Notice that only half of the hyperbola is visible. Why is that? Hint: It has to do with how you defined your circles.
Finish it up!
Add in a few more lines of commands to create the other half of the hyperbola.