The Locus of Points Equidistant from Two Circles
- Author:
- Ryan Hirst
- Topic:
- Circle, Equations, Linear Equations
The locus of points equidistant from two circles.
There are two solutions: a single branch of a hyperbola (orange), and an ellipse (blue).
Case I: If one circle completely encloses the other, there is one solution: an ellipse.
Case II: If the two circles are entirely outside one another, there is one solution: the branch of the hyperbola closer to the midpoint of the smaller circle.
Case III: If the two circles intersect, both solutions occur simultaneously.
Please let me know if you would like more information about the construction; some of the details are not obvious, even from the full worksheet.