key term - Semi-minor Axis

Definition

The semi-minor axis is one of the defining characteristics of an ellipse, which is a closed, two-dimensional shape that resembles an elongated circle. The semi-minor axis is the shorter of the two axes that determine the size and shape of the ellipse.

5 Must Know Facts For Your Next Test

1. The semi-minor axis is always perpendicular to the major axis and intersects the center of the ellipse.
2. The length of the semi-minor axis, along with the length of the major axis, determines the overall size and shape of the ellipse.
3. As the semi-minor axis increases in length, the ellipse becomes more circular, while a shorter semi-minor axis results in a more elongated ellipse.
4. The semi-minor axis, along with the major axis, can be used to calculate the area of an ellipse using the formula: $\pi \times a \times b$, where $a$ is the length of the major axis and $b$ is the length of the semi-minor axis.
5. The eccentricity of an ellipse is inversely related to the ratio of the semi-minor axis to the major axis, with a higher eccentricity indicating a more elongated shape.

Review Questions

• Explain the relationship between the semi-minor axis and the overall shape of an ellipse.
  • The length of the semi-minor axis is directly related to the shape of the ellipse. A longer semi-minor axis results in a more circular ellipse, while a shorter semi-minor axis creates a more elongated, or flattened, ellipse. The ratio of the semi-minor axis to the major axis determines the eccentricity of the ellipse, with a higher eccentricity indicating a more elongated shape.
• Describe how the semi-minor axis is used to calculate the area of an ellipse.
  • The semi-minor axis, along with the major axis, can be used to calculate the area of an ellipse using the formula: $\pi \times a \times b$, where $a$ is the length of the major axis and $b$ is the length of the semi-minor axis. This formula takes into account the two defining axes of the ellipse to determine its total area. The semi-minor axis is a crucial component of this calculation, as it directly impacts the overall size and shape of the ellipse.
• Analyze the role of the semi-minor axis in the context of the broader properties of an ellipse.
  • The semi-minor axis is a fundamental characteristic of an ellipse that, along with the major axis, defines the shape and size of the two-dimensional figure. The semi-minor axis is perpendicular to the major axis and intersects the center of the ellipse. The ratio of the semi-minor axis to the major axis determines the eccentricity of the ellipse, which is a measure of how elongated or flattened the shape is. Understanding the semi-minor axis and its relationship to the other properties of an ellipse is crucial for accurately describing, analyzing, and working with this important geometric shape.

Related terms

Ellipse:

A closed, two-dimensional shape that is defined by two axes: the major axis and the minor axis. The semi-minor axis is half the length of the minor axis.

Major Axis:

The longer of the two axes that define the size and shape of an ellipse.

Eccentricity:

A measure of how elongated or flattened an ellipse is, calculated as the ratio of the distance between the foci to the length of the major axis.