Double Cone

A double cone (or double-napped cone) is the surface you get by spinning one straight line around another.

Take a fixed line $l$ (we will call it the axis) and a second line $m$ that crosses $l$ at a fixed point $V$, making a constant acute angle $\theta$ with it. Now imagine rotating $m$ all the way around $l$, always keeping that same angle $\theta$. The surface swept out by $m$ as it spins is the double cone.

• $V$, the point where the two lines cross, is called the vertex of the cone.
• $l$ itself is called the axis of the cone.
• Any position of the rotating line $m$ (at any instant during the spin) is called a generator of the cone. …