Question

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 miles by 8 miles. Find an equation for the ellipse if the path is to touch the center of the property line on all 4 sides

Answer 1

a = 8/2 = 4
b = 10/2 = 5
Equation of ellipse is given by x^2/a^2 + y^2/b^2 = 1
x^2/4^2 + y^2/5^2 = 1
x^2/16 + y^2/25 = 1

Answer 2

The answer above is mostly correct, HOWEVER The ellipse is a vertical ellipse and therefore uses the equation (x^2/b^2)+(y^2/a^2)=1

a=10/2=5

b=8/2=4

put it in the equation and it is (x^2/4^2)+(y^2/5^2)=1

Simplify and the answer is (x^2/16)+(y^2/25)=1