Eccentricity

Definition

Eccentricity measures the deviation of a conic section from being circular. It is denoted by $e$ and determines the shape of the conic.

5 Must Know Facts For Your Next Test

1. For a circle, the eccentricity $e = 0$.
2. For an ellipse, $0 < e < 1$.
3. For a parabola, $e = 1$.
4. For a hyperbola, $e > 1$.
5. The eccentricity is calculated using the formula $e = \frac{c}{a}$ where $c$ is the distance from the center to the focus and $a$ is the semi-major axis length.

Review Questions

• What is the eccentricity of a hyperbola?
• How does eccentricity help differentiate between different types of conic sections?
• Calculate the eccentricity of an ellipse with semi-major axis length 5 and distance from center to focus 3.

Related terms

Conic Section: A curve obtained as the intersection of a cone with a plane. Examples include circles, ellipses, parabolas, and hyperbolas.

Semi-Major Axis: The longest diameter of an ellipse, extending from one side to another through its center.

Focus: One of the fixed points used to define a conic section. For ellipses and hyperbolas, there are two foci.