Conic sections in one of the important areas of mathematics. We can observe the conic shapes in many real life applicationsThe study of formation of conic sections can be investigated following classical Greek mathematicians, ordinarily to Applonious. The name ‘conic section’ comes from the fact that the principal types of conic sections, such as hyperbolas and parabolas, are formed by cutting a right circular cone with a plane. However, the most recent publications and textbooks on calculus quit from this geometric approach. Alternatively, conic sections are defined as some types of loci and studied with the help of analytic geometry.
In mathematics, a conic section or simply called a conic is defined as a curve that is obtained from the intersection of a cone’s surface with a plane. The three main types of conic sections are namely the parabola, the hyperbola, and the ellipse. However, there is another type of conic section called the circle. It is considered a particular case of the ellipse though sometimes this is called historically as the fourth type. All these types of conic sections will be introduced using some approaches in the higher classes of education.
If we consider a plane’s intersection with a cone, the obtained section from this is described as a conic section. Consequently, conic sections are the curves achieved from the intersection of a right circular cone with a plane. We get different types of conic sections depending on the intersecting plane’s position concerning the cone. It also considers the angle made by it with the cone’s vertical axis. The intersection of the cone with the plane can occur either at the vertex of the cone. Sometimes it will appear at any other part of the nappe either above or below with respect to the vertex.
A new system to introduce conic sections is the intersections of two cones. Here, the vertices of these two cones will be taken as the conic section’s inherent foci. The directrix of a conic exists associated with each of the intrinsic foci. All the identified properties of conic sections still hold the fixed foci and their associated directrixes in this innovative procedure. This new procedure looks more straightforward and natural than the classical geometric and analytical techniques for describing conic sections and proving the respective properties. It is also possible to derive other parameters of these conics to answer the questions like what is the general equation of ellipse? This type of derivations are useful in defining the parameters of conics.
We know that every geometric shape has specific applications in some fields along with the real-life application. Similarly, all the conic section curves have a wide range of applications in planetary motion, telescopes and antennas, reflectors in flashlights, automobile headlights, etc. For example, we use a parabolic mirror as the reflector in making a searchlight, with a bulb at the focus. Also, a similar structure is designed for a parabolic microphone. The curves of conic sections are essential tools for the present-day research of outer space and the examination into the performance of atomic particles.