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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?

An ellipticalshaped 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 class=

Respuesta :

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

[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1,a>b[/tex]

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

[tex]\begin{gathered} a^2=289,b^2=169 \\ \Rightarrow a=17,b=13 \end{gathered}[/tex]

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

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