A retired math teacher decides to present her husband with a...

Name: Problem 66, Chapter 9: Precalculus
Uploaded: 2020-08-13T16:03:47-08:00
Duration: 3 min 9 s
Channel: Subham Jyoti Mishra
Description: A retired math teacher decides to present her husband with a beautiful elliptical garden to help celebrate their 50 th anniversary. The ellipse is to be 8 m long and 5 m across, with decorative fountains located at the foci. How far from the center of the ellipse should the fountains be located (round to the nearest 100 th of a meter)? How far apart are the fountains?

A retired math teacher decides to present her husband with a beautiful elliptical garden to help celebrate their 50 th anniversary. The ellipse is to be 8 m long and 5 m across, with decorative fountains located at the foci. How far from the center of the ellipse should the fountains be located (round to the nearest 100 th of a meter)? How far apart are the fountains?

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Key Concepts

Ellipse Geometry

An ellipse is a conic section defined as the set of points in a plane such that the sum of the distances from any point on the ellipse to two fixed points (called foci) is constant. This property is the foundation for many applications in geometry and physics, where understanding the shape and its characteristics is essential.

Axes of an Ellipse

The ellipse has two principal axes: the major axis, which is the longest diameter, and the minor axis, which is the shortest. The lengths of these axes are fundamental in determining the overall shape and size of the ellipse. The semi-major axis (half of the major axis) and the semi-minor axis (half of the minor axis) are particularly important as they are used in various formulas to analyze the ellipse's properties.

Foci of an Ellipse

The foci are two fixed points located along the major axis of the ellipse. The distance from the center of the ellipse to either focus can be determined using the relationship c = ?(a² - b²), where a is the length of the semi-major axis and b is the length of the semi-minor axis. This relationship is crucial for quantifying distances and understanding the ellipse's structure.

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