A **cone** is a 3 dimensional object. It is obtained when one of the pair of intersecting lines is rotated about the other line in such a way that the angle between the lines is constant.

The point of intersection of lines is known as the **vertex** of cone, the fixed line is known as the **axis** and the rotating line is known as the **generator** of the cone. We get 2 equal portions, which are known as **nappes**.

When a plane intersects a cone, we get a **conic section**. It depends on the inclination of the plane w.r.t. the axis.

If the plane is **perpendicular** to the axis, we get a **circle**.

If the plane is **NOT parallel** to the generator, passes through **only 1 nappe** and does **not** contain the **vertex**, we get an **ellipse**.

If the plane is **parallel** to the generator and does **not** contain the vertex, we get a **parabola**.

If the plane is **NOT parallel** to the generator, passes through **both nappes** and does **not** contain the **vertex**, we get a **hyperbola**.

If the plane passes through the vertex of cone and contains the axis, we get a **pair of straight lines**.