Conic Sections | CK-12 Foundation
Conics

Aoa!

 After reading this you will be able to understand the concept of conic section.

So, firstly we will discuss about word conic section.

The word conics describe a concept of a cone. Now you must understand that what a cone is.

Cone:

  A cone is a three dimensional geometrical shape which tappers smoothly from its circular base towards its point.

Now we will define section.

Section:

       Section means that parts. So, after that we concluded that the word Conic section means that the parts of a cone.

After this you must understand the concept of plane that what is a plane???

Plane:

      A two (2) dimensional surface with zero thickness and which extends infinitely that surface is called as plane.

Now we will discuss that what Double Right Circular Cone is.

Double Right Circular Cone:

When a straight line intersects a fixed vertical line from a fixed point and rotates about that point then we obtained a surface which is called as Double Right Circular Cone.

Now we will define that what Conic Section is.

Conic Section:

When a plane intersects a Double Right Circular Cone, we obtain a 2 two Dimensional curves of different types So, those curves are called as Conics or Conic Section.

Now we will discuss about the types of conics or conic section.

  1. Ellipse
  2. Circle(Special case of ellipse)
  3. Parabola
  4. Hyperbola

Ellipse:

When a plane intersects the double right circular cone in such a way that angle between axis and plane is greater than vertex angle or 90 degree so, we obtain a curve called ellipse.

Circle:

When the intersecting plane is perpendicular to the axis of the cone so, we obtained a closed curve called as circle

                                         Or

When angle between axis of cone and plane is 90 degree then a curve is obtained that is called as Circle.

Parabola:

When an intersecting plane is exactly parallel to generator line we can get a open curve called as Parabola.

                                 Or

When angle between axis of cone is greater than 90 degree so, it is formed as Parabola.

Hyperbola:

When axis of cone and plane are parallel to each other and cut the cone then a curve is obtained called as Hyperbola.

                                      Or

When plane intersects a double right circular cone in such a way that angle between axis and plane is less than vertex angle so, we obtain a curve called as Hyperbola.

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