Question

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



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

These are my steps so far, what else do I do?

Center: (0,0)

x^2/a^2 + y^2/b^2 = 1
= x^2/16 + y^2/25 = 1

Answer 2

You are using the wrong formula for an ellipse with the major axis along the y axis.

Use this one instead.\[\frac{ x ^{2} }{ b ^{2} }+\frac{ y ^{2} }{ a ^{2}}=1\]

Otherwise, you would have correct.