Construct a segment through point C and the center of the circle, A. Construct another point D within the circle. Find the midpoint, F, of this segment. Trace that point, H, as the point C travels along the circumference of the circle. The following is the picture with the appropriate labels. D and A are the foci, and V1-V4 are the vertices.
H is the point that defines the ellipse.
Click here to view the GSP file that demonstrates this. As D is moved within the circle, you will get a different ellipse as seen in the following picture. The equation of this hyberbola is The equation of this hyberbola is . A more geometric definition of a hyperbola is the set of all points in the plane, the difference of whose distances from two fixed points is a positive constant. How can we use the GSP construction above to create a hyperbola.