Johannes Kepler said, “A parabola is an ellipse with a focus at infinity.” On its face, this statement is nonsense. What does it mean for a focus to be “at” a point that is not defined? In this animation, points on the plane are associated with points on a sphere by stereographic projection. The north pole of the sphere corresponds to the point at infinity. This is the one point compactification of the plane. Curves in the plane correspond to curves on the sphere. In particular, a family of ellipses in the plane with one focus that tends to infinity is displayed. On the sphere, when the focus is at the point at infinity, the curve corresponds exactly to a parabola in the plane. The focus on the sphere is then sent beyond infinity, over the top. The corresponding curves in the plane are hyperbolas. In this sense, hyperbolas are ellipses where one focus has been sent to infinity and then back from the other side, just as Kepler described. Using the one point compactification, we can make sense of Kepler’s descriptions of the conic sections.