What is Eccentricity?
In the conic chapter, we learn that there are 4 different types of shapes which are parabola, hyperbola, ellipse, and circle. They all are related to conics. When we talk about conic sections, we go back in 350 B.C when the Greek civilization discovered about different derived shapes from conic. They sliced the double cone in different ways and found 4 new shapes. If you want to learn more about conic then click here.
So, what is the difference between all these shapes? You must be thinking the structure of shape is different and you are correct, however, how you can differentiate in the world of mathematics? If you notice, they all are somewhere similar to the circle. For example, take a look at an ellipse. If you stretch a circle from the abscissa or ordinate, you will get an ellipse. Basically, an ellipse is a compressed circle. Like that, almost all the shapes are similar to a circle. You can't call them a circle since they are different shapes and possess different properties. This is where we introduce you to Eccentricity.
What is eccentricity? In many books, you will find this definition "Eccentricity measures the degree of the opening of the branches of the shapes". Let us make it easier for you. Eccentricity reveals how un-circular the curve is. Finding eccentricity is very easy but you need to understand the concept behind that.
When we find eccentricity, we always take a reference and find values relative to that reference. So, which shape we should take as a reference? The Greek mathematicians have already done the hard part. After all the calculations and intense study, they took circle as a frame of reference. This means that whenever you will find the eccentricity of any shape, you are measuring eccentricity of the shape with the reference of a circle. In simple words, you will be determining how similar your shape is to circle. If the eccentricity value is low then it means that the shape is more similar to the circle.
If we take the circle as the frame of reference then what will be the eccentric value of circle? The eccentric value of the circle is zero. It means that if the shape's eccentric value is zero, it is a perfect circle. However, if the eccentric value is, for example, 0.002 then you can't say it is a circle but if you draw this shape on a graph, it will be difficult for you to declare either the shape is a circle or ellipse. That is why eccentricity is important.