The Inverse of a Hyperbola
- Irina Boyadzhiev
Given is a hyperbola, defined by its foci points and , and point . We perform inversion with respect to the circle with center and radius r. Point D is a point on the circle. We can change the radius by dragging . Point is a random point on the hyperbola. Point is the image of under inversion with respect to the above circle (). As moves along the hyperbola, will draw the locus of the inverse of the hyperbola. If the center of the circle is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
- Move point or to change the hyperbola, and see the changes in the Limaçon.
- Drag point D to change the radius of the circle and see how this affects the Limaçon.
- Move the center of the circle to the center of the hyperbola. What is the inverse in this case?
- Continue to experiment by dragging the center of the circle to other locations.