# Section of a right circular cone

- Author:
- Šárka Voráčová

- Topic:
- Cone, Conic Sections, Solids or 3D Shapes

A conic is the curve obtained as the intersection of a plane with the surface of a double cone (a cone with two nappes). Planes that pass through the vertex of the cone will intersect the cone in a point, a line or a pair of intersecting lines. These are called degenerate conics.
The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone.
If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.
In the remaining case, the figure is a hyperbola: the plane intersects both halves of the cone, producing two separate unbounded curves.

Rigt circular cone with height h = 5 and radius of the base r = 2 is intersected by a plane with the slope k. Determine the slope for parabolic section.