1. 11.1: Ellipses

2. Conics The conics get their name from the fact that they can be formed by passing a plane through a double-napped cone (two right circular cones placed together, nose-to-nose).

3. Analytic Geometry The study of the geometric properties of objects using a coordinate system is called analytic geometry (hence, the title of chapter 11).

4. Applications of Ellipses If an ellipse is rotated about the major axis, you obtain a football.

5. Applications of Ellipses The path of planets in orbit is elliptical in shape.

6. Definition of the Ellipse An ellipse is the set of all points such that the sum of the distance from P to F1 and P to F2 is k. PF1 + PF2 = k (F1 and F2 are the foci)