Circular Conic Section
The circle can be extended as a special case of an ellipse, the cutting plane here is parallel to the cone base. This center of the circle is the focus and the radius of the circles is also constant. The value of eccentricity of a circle is always zero that is
e = 0
Now, if we assume that the center of the circle is situated in the Cartesian plane and is marked with the coordinates (h, k) where ‘h’ is the x-coordinate and ‘k’ is the y-coordinate, respectively then the general form of the equation of the circle can be expressed in the following manner.
(x − h)2 + (y − k)2 = r2
Here ‘h’ and ‘k’ are the coordinates of the origin, ‘r’ is the radius of the circle which is always constantly nature, and x and y are the coordinates of any other point on the circle.
Use Trigonometric Substitution and Trigonometric Identity to determine the Circumference of a Circle of Radius 3.
When any two-dimensional or three-dimensional plane is being intersected and cut then there are curves obtained, which are known as conic sections. In the case of a cone, there are two identical conical shapes, which are also known as capes. The shape of these conical shapes in the cone depends upon the angle that is opting in as a result of the cut between the plane and the cone. Various shapes can be obtained depending upon the difference in the curve sizes which are circle, hyperbola, ellipse, and parabola we can study these shapes in detail, wherein
- The ellipse is one of the conic sections, which is formed as a result of the intersection of a plane with the cone at an angle.
- The circle is considered to be a conic section where the intersection happens parallel to the cone base and it can be considered to be a special type of ellipse.
- Also, hyperbola formation occurs when the plane is parallel to the cone axis and the intersection happens with both the names of the double cone.
- Lastly, we obtain a parabola when the intersecting plane cuts the surface of the cone at an angle.
The following diagram represents the various types of conic sections that are available depending on the difference in the cuts between the intersecting surface and the cone and its necks.
In this article, we will focus on the conical section of the circle. First, the circle has the following properties,