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# Answer to Question #45105 in Analytic Geometry for shasha

Question #45105
An elliptical riding path is to be built on a rectangular piece of property as shown below.

A vertical ellipse is shown centered on the coordinate plane, surrounded by a rectangle of equal length and width.

The rectangular piece of property measures 10 mi by 4 mi. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides.

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Assignment Expert
13.07.16, 15:08

You are right. If the ellipse is horizontal, then the answer is (x² / 25) + (y² / 4) = 1.
If the ellipse is vertical, then the answer is (x² / 4) + (y² / 25) = 1.

Patricia
09.07.16, 05:26

This is partially right. The question specifies that it is a vertical ellipse. The answer above shows a horizontal ellipse. The right answer would be (x² / 4) + (y² / 25) = 1.