The current high school curriculum calls for students to study and understand the underlying principles of conic sections including ellipses and hyperbolas. As we have seen, the locus of the center of the circle tangent to two given circles is an ellipse or hyperbola, depending on the placement of the given circles.

We begin teaching our students about ellipses with the discussion of this picture. F1 and F2 are the foci of the ellipse and P is any point on the ellipse.

P*F1 + P*F2 = k where k is some constant.

However, it is important for students to have a deeper understanding of how to genertate the above illustration and why the equation is true. The construction of circle tangent to two given circles clearly demonstrates both of these concepts.

We begin teaching our students about hyperbolas with the discussion of this picture. F1 and F2 are the foci of the hyperbola and P is any point on the hyperbola.

To explore the locus as a hyperbola, click here.