Question

An elliptical-shaped path surrounds a garden, modeled by quantity x minus 20 end quantity squared over 169 plus quantity y minus 18 end quantity squared over 289 equals 1 comma where all measurements are in feet. What is the maximum distance between any two persons on the path, and what key feature does this represent?

Answer 1

In general, the equation of an ellipse centered at (h,k) and axis equal to a and b, and parallel to the y-axis is

`((x-h)^2)/(b^2)+((y-k)^2)/(a^2)=1,a>b`

And the maximum distance between two points on the ellipse is equal to the length of the major axis; in our case,

`\begin{gathered} a^2=289,b^2=169 \\ \Rightarrow a=17,b=13 \end{gathered}`

Therefore, the answer is 17 feet, the major axis.