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Concept

Conic Section

A conic section, also called a conic, is a curve that follows the intersection between a plane and a cone. The three types of conic section are the ellipse, the parabola, and the hyperbola. When a plane cuts the cone at an angle to the base, it results in an ellipse.
Plane cutting a cone with an ellipse-shaped intersection
When the plane of an ellipse is parallel to the base of the cone, a circle is formed. When the intersecting plane is parallel to the cone's side, leading to an open-ended curve, a parabola is formed.
Plane cutting a cone with a parabola-shaped intersection
In other cases, the plane can also intersect two cones at once, where one cone is the mirror image of the other cone. This creates a hyperbola.
Intersection between two cones and a plane forming a hyperbola
Each conic section has its own unique equation and geometric properties. The general equation for conic sections can represent different types of conics depending on the values of its constants and their relationships.
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