## 2.19. The Conic Sections

A **right
circular cone** can be generated by rotating a **generator **line *G* about an
**axis** *A* with which it intersects at an angle
0<θ<
π
4
at the **vertex**
*P*.
Each of the upper and lower
portions is called a **nappe** of the
cone. The curves obtained by the
intersection of a plane with the surface of the cone are called **conic sections** or simply **conics**.
Depending on the angle of the plane, one can obtain 3 types of curves
[see Fig.2.9]. With the help of the
icecream-cone proof [see text], they can be identified with the **parabola**, **ellipse** and **hyperbola**
defined in Fig.2.10.