The minor axis of an ellipse is the shorter of the two perpendicular lines that intersect at the center of the ellipse, dividing it into two equal halves. It is one of the defining characteristics of an elliptical shape.
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The minor axis determines the height or vertical dimension of an ellipse.
The ratio of the minor axis to the major axis is the eccentricity of the ellipse.
The minor axis is always perpendicular to the major axis and intersects it at the center of the ellipse.
The length of the minor axis, along with the length of the major axis, can be used to calculate the area of an ellipse.
The minor axis is one of the key parameters used to define and describe the shape of an ellipse.
Review Questions
Explain the relationship between the minor axis and the major axis of an ellipse.
The minor axis and major axis of an ellipse are perpendicular to each other and intersect at the center of the ellipse. The minor axis represents the shorter of the two dimensions, while the major axis represents the longer dimension. The ratio of the minor axis to the major axis is the eccentricity of the ellipse, which determines how much the shape deviates from a perfect circle.
Describe how the minor axis is used to calculate the area of an ellipse.
The area of an ellipse is calculated using the formula $A = \pi ab$, where $a$ is the length of the major axis and $b$ is the length of the minor axis. The minor axis, along with the major axis, is a key parameter in determining the overall size and shape of the ellipse. By knowing the lengths of both the minor and major axes, you can accurately calculate the area of the ellipse.
Analyze how changes in the minor axis affect the overall shape and properties of an ellipse.
Varying the length of the minor axis while keeping the major axis constant will alter the eccentricity of the ellipse. As the minor axis becomes shorter relative to the major axis, the eccentricity increases, and the ellipse becomes more elongated and oblong. Conversely, as the minor axis becomes longer, the eccentricity decreases, and the ellipse approaches a more circular shape. These changes in the minor axis affect the overall appearance, area, and other geometric properties of the ellipse.
The major axis of an ellipse is the longer of the two perpendicular lines that intersect at the center of the ellipse, dividing it into two equal halves.
Eccentricity is a measure of how much an ellipse deviates from a perfect circle, with a value between 0 and 1.
Focal Points: The focal points of an ellipse are two points on the major axis that are equidistant from the center, and the sum of the distances from any point on the ellipse to the focal points is constant.