Eccentricity – Conic Section

Photo of author

( — October 23, 2021) —

Nowadays, the importance of studying and learning mathematics has taken over all the other subjects. Maths is a subject that promotes logical reasoning in students. This subject also helps in effective and efficient mind development as well as thinking. 

Mathematics also assists one and helps in preventing chaos and hence promote orderliness. It is also known to be a significant subject in the success of one’s career. Most jobs and higher education require math as a major subject in all fields.

We need to focus on this subject to increase the opportunities in the future. Mathematics is divided into 4 main sub-sections, one of which is geometry. Geometry is a huge subject to study that also develops the interest of many students. 

This includes the study of graphs, various equations, lines, and shapes, etc. Mathematical equations include a concept namely eccentricity. This concept characterizes the shape of a particular curve and is a non-negative real number. It can be recognized as a measure of how much the conic section is deviated from being a circular shape. Let us now discuss more this topic:

  1. The Eccentricity of an ellipse can be explained as to how flat or circular the shape of the ellipse is. The Eccentricity of an equation can be referred to according to its shape such as the eccentricity of a circle is zero and it is a whole round. Whereas the eccentricity of a parabola is one. The eccentricity of an ellipse is generally somewhere between that of a circle and that of a parabola which means that the eccentricity of an ellipse is between zero and one. For hyperbola, the eccentricity is always more than one. The eccentricity of a line is infinite as it is not curved in any way.

  2. There are various formulas used to find out the eccentricity of different curves and shapes. To begin with, the eccentricity of an ellipse is calculated by dividing the distance between the fixed points by the length of the major axis, and hence the formula to find out the eccentricity of an ellipse turns out to bee = (1-b2/a2)1/2. If the eccentricity turns out to be zero, then the shape is known to be a circle instead of an ellipse. Generally, the equation for eccentricity is x2 = 4ay which is always equal to one.

  3. The basic formulae to calculate the eccentricity of any conic section is known to be e = c/a, where c is the distance of the center from a fixed point and a is the distance of the center from the vertex.

To conclude, eccentricity is the measure of the deviation of a curve from being a circle. This consists of the topics parabola, hyperbola, and ellipse equations. It is a concept highly based on the skills and effort you put in. 

It also requires you to remember the formulas and practice various questions. Achieving regularity isn’t very easy unless you join some tutorial classes that can provide you with effective and efficient efforts to shine up your skills and efforts to accomplish better and improved results.

 Cuemath classes can assist you in achieving your desired goals and excel in your geometry as well as maths. One can also join these classes to learn and practice coding. The foremost advantage of these classes is that they provide you with online classes which helps in studying from the comfort of your home which increases your efficiency to learn. Therefore, it’s a must for every student to join these classes and upgrade their academic performance.