Question

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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.

Answer 1

If the ellipse is vertical, then the answer is (x² / 4) + (y² / 25) = 1.
I hope this helps :)

Answer 2

Answer:

For those who need a written explanation:

Step-by-step explanation:

Since the ellipse is vertical, we use the equation (x^2/b^2)+(y^2/a^2)=1. a=10/2, or 5 while b=4/2, or 2. Plug these into the equation to have (x^2/2^2)+(y^2/5^2)=1. Now simplify to get: (x^2/4)+(y^2/25)=1 which is our answer.