Question

An elliptical-shaped path surrounds a garden, modeled by quantity x minus 22 end quantity squared over 225 plus quantity y minus 26 end quantity squared over 324 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

The ellipse has 2 axis, the minor and the major axis,

The major axis is denoted in blue color and the minor axis in purple color. By comparing our equation with the general equation of the ellipse:

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

where the lenght of the major axis is given by

`\text{lenght major axis=2b}`

Fron the given equation, we can note that

`b=\sqrt[]{324}=18`

Therefore, the lenght of the major axis is 36 feet. Therefore, the maximum distance between any two persons is 36 feet corresponding to the major axis, which is option 3 from top to bottom