Sample: My Hyperbola Lab
With the use of the resource http://jwilson.coe.uga.edu/ , I was able to create this hyperbola sketch.
First, was the construction a "circle with center through point", the center being focus1 along with a point on the outside of the circle, named focus2.
A point was made on the object (point D) and a line is made from focus1 and point D.
Next, a segment was made from point D to focus2, along with the midpoint of this segment.
A perpendicular line was created from this line, and added a point (point F) to the intersection of this line and the first line.
Lastly, I turned on the trace and animation to the point... and taaaa daaa, a hyperbola!