Types of Conic Sections

TYPES OF CONIC SECTIONS

Conic sections (or) simply conics are obtained by cutting a right circular cone at different positions as shown below.

By referring the views shown above, Conic sections are defined as below:

Circle is a conic section obtained by cutting a right circular cone in such a way that the cutting plane is perpendicular to the axis of the cone. 

Ellipse is a conic section obtained by cutting a right circular cone in such a way that the cutting plane is inclined to the axis of the cone and the cutting plane cuts all the generators.

Parabola is a conic section obtained by cutting a right circular cone in such a way that the cutting plane is inclined to the axis of the cone and parallel to one of the generators. The inclination of cutting plane is equal to half of the apex angle of cone.

Hyperbola is a conic section obtained by cutting a right circular cone in such a way that the cutting plane is inclined to the axis by an angle smaller than half of the apex angle of cone.