The conic section represents any curve that is obtained when a cone touches a plane. It covers an important portion of Mathematics. Questions in competitive examinations are based on this critical portion. It is a spectacular branch of geometry that represents special figures like ellipse and parabola. There are many properties related to conic figures that must be studied in detail to obtain suitable results. All these properties are known as conic properties. Many eminent scholars of Mathematics have carried out detailed research on this topic and have obtained fascinating conclusions. These facts have been utilized to solve a variety of questions.
Various conic parameters need to be studied in detail to understand the basics of the conic section. If these parameters are not understood clearly then it may lead to many difficulties when one tries to solve the questions. These parameters are namely eccentricity, focus, directrix, principal axis, latus rectum, focal parameter, the major axis, and the minor axis. All these parameters are discussed in detail while studying this fascinating topic.
A conic section can be clearly defined in the terms of plane geometry. It is the locus of all the respective points whose distance to a fixed point that is termed as the focus is a constant multiple of the distance between the different points and any given line. The constant multiple is referred to as the eccentric factor while the distance is termed as the directrix.
Based on the values of the conic parameters, various conic figures are formulated. It is important to remember the basic properties related to each of the figures. This article discusses the different figures and the basic postulates related to these figures.
The fundamental figures of the conic section along with their properties:
● Hyperbola: The hyperbola is one of the basic figures related to the conic section. It is basically a smooth curve that lies in a plane. Numerous geometric equations are used to identify a hyperbola and solve the questions related to it. This exemplary figure comprises two major components that are referred to as the connected components. This figure is formed when a plane intersects a double cone. The ratio of the distance between the center and the focus to the distance between any vertex and the center is greater than one. This is the most basic way to identify a hyperbola. One must practice numerous questions to gain expertise on this topic.
● Ellipse: This is a plane curve that surrounds two points on a curve. It has been observed that the sum of the distance between two focal points of this exemplary figure is always equivalent to a constant. Ellipse refers to the closed type of conic section. This figure has many similarities to other conic figures. This figure finds application in many crucial parts of Physics and Engineering. It is quite surprising to know that the angled cross-section of a cylinder also refers to an ellipse. The eccentricity for an ellipse is always less than one.
● Parabola: This is another incredible conic figure with a wide array of applications. It is generally a u-shaped curve that is formed by the intersection of a right circular conical surface with a plane that is parallel to another respective plane that is a tangent to the conical surface. This figure has a variety of practical uses because of its reflective property. The eccentricity of a parabola is equivalent to one.
This article aims to cover the different aspects of the three different conic figures. They form a crucial part of Mathematics known as the conic section. It is very important from the examination perspective. Students can take the help of Cuemath to solve the complex questions related to this portion. It is a magnificent online forum that has been designed to resolve the doubts of needy students related to coding and Mathematics.