Journal of the Mathematics Council of the Alberta Teachers’ Association
Volume 43 Issue 2, June 2006
33 – 36
Where Is the Directrix of a Circle?
David E Dobbs
The conic sections (parabola, ellipse and hyperbola) get their name from the fact that each can be obtained as the intersection of a plane with a double-napped right circular cone. By changing the position of the plane relative to the cone, one finds that certain positions produce an intersection that is typically referred to as a degenerate or limiting case of a conic, such as a point, a line, two intersecting lines or a circle. In particular, a circle can thus be viewed as a limiting case of an ellipse (see, for instance, Dobbs and Peterson 1993, Figure 8.1, 441 ).
