In your own words, define an ellipse and write the equation...

Name: Problem 143, Chapter 11: Intermediate Algebra
Uploaded: 2022-09-30T16:15:31-08:00
Channel: Nicole Hoffman
Description: In your own words, define an ellipse and write the equation of an ellipse centered at the origin in standard form. Draw a sketch of the ellipse labeling the center, vertices and major and minor axes.

In your own words, define an ellipse and write the equation of an ellipse centered at the origin in standard form. Draw a sketch of the ellipse labeling the center, vertices and major and minor axes.

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Key Concepts

Graphical Representation and Key Features

When graphing an ellipse, it is essential to mark its center, vertices, and the major and minor axes. The center serves as the midpoint of the ellipse, while the vertices are the points where the ellipse intersects the major axis, representing its farthest extent from the center. The major axis is the longest diameter and the minor axis is the shortest, which are perpendicular to each other, providing a clear visual structure of the ellipse's geometry.

Ellipse

An ellipse is a type of conic section defined as the set of all points in a plane for which the sum of the distances from two fixed points (the foci) is constant. This geometric definition emphasizes its unique, closed curved shape that is symmetric and, depending on the lengths of its axes, can be elongated in one direction.

Standard Form Equation of an Ellipse

The standard form equation of an ellipse centered at the origin is expressed as (x²/a²) + (y²/b²) = 1, where a and b are the lengths of the semi-major and semi-minor axes, respectively. This form is crucial for understanding the algebraic representation of the ellipse and for determining its orientation and dimensions based on the relative sizes of a and b.

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