The maximum distance between any two points of the ellipse is 34 feet.
The maximum distance between any two points of a ellipse is the maximum distance between the ends of the ellipse along the longest axis, which is parallel to the y-axis in this case.
In addition, the equation of the ellipse in standard form is defined by this formula:
[tex]\frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} = 1[/tex] (1)
Where:
Hence, the maximum distance ([tex]d_{max}[/tex]), in feet, is calculated by this formula:
[tex]d_{max} = 2\cdot b[/tex] (2)
If we know that [tex]b = 17[/tex], then the maximum distance between any two points of the ellipse is:
[tex]d_{max} = 2\cdot (17\,ft)[/tex]
[tex]d_{max} = 34\,ft[/tex]
The maximum distance between any two points of the ellipse is 34 feet. [tex]\blacksquare[/tex]
The statement is incomplete and poorly formatted, correct form is presented below:
An elliptical-shaped path surrounds a garden, modeled by [tex]\frac{(x-20)^{2}}{169} + \frac{(y-18)^{2}}{289} = 1[/tex], where all measurements are in feet. What is the maximum distance between any two points of the path.
To learn more on ellipses, we kindly invite to check this verified question: https://brainly.com/question/19507943
