For conic sections, we can define them in terms of conic eccentricity \(e\). It describes the shape of a conic.
Defining Eccentricity
We begin by defining what eccentricity \(e\) is. It is a number from 0 to infinity. At its basic, it is the ratio of \(c\) and \(a\):
\(e=\frac{c}{a}\)
What is \(c\) and \(a\)? Generally speaking, we can define it as the following:
- Linear eccentricity \(c\) is the length between the center of the conic and its focus
- Semi-major distance \(a\) is the half distance between the conic's vertices.
These distances \(c\) and \(a\) will depend on the conic:
Interpreting Eccentricity
When we have an eccentricity value \(e\), how do we interpret it? The following table shows the meaning:
From this table, we can observe the following: when we have an eccentricity of 0, it is a circle. As \(e\) grows larger and larger, the section deviates from being a circle. When \(e\) approaches infinity, it will eventually be a line.
Summary
For conic sections, we can define them in terms of conic eccentricity \(e\).
Conic eccentricity \(e\) is a number from 0 to infinity. We can define it mathematically as a ratio of linear eccentricity \(c\) and semi-major distance \(a\).
When we have an eccentricity of 0, it is a circle. As \(e\) grows larger and larger, the section deviates from being a circle.
