Based on material learned earlier in the course. The purpose...

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. Find an equation of an ellipse if the center is at the origin, the length of the major axis is 20 along the $x$ -axis, and the length of the minor axis is 12 .

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Find an equation of an ellipse if the center is at the origin, the length of the major axis is 20 along the $x$ -axis, and the length of the minor axis is 12 .

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Key Concepts

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 to two fixed points (the foci) is constant. It is characterized by its smooth, closed, oval shape and has specific geometric properties that distinguish it from other conic sections like parabolas and hyperbolas.

Standard Equation of an Ellipse

The standard form of an ellipse’s equation provides a way to represent the ellipse algebraically, particularly when it is centered at the origin. For an ellipse with its major and minor axes aligned with the coordinate axes, the equation is written as x²/a² + y²/b² = 1, where a and b are the semi-major and semi-minor axis lengths, respectively.

Major and Minor Axes

The major axis of an ellipse is its longest diameter, while the minor axis is its shortest. The lengths of these axes determine the ellipse's dimensions, with the semi-major axis (a) being half the length of the major axis and the semi-minor axis (b) being half the length of the minor axis. These values are critical in determining the shape of the ellipse and its algebraic representation.

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