The <em>maximum</em> distance between any two points of the ellipse is 34 feet.
<h3>Procedure - Determination of the distance between two points of a ellipse</h3>
The maximum distance between any two points of a ellipse is the <em>maximum</em> distance between the ends of the ellipse along the <em>longest</em> axis, which is parallel to the y-axis in this case.
In addition, the equation of the ellipse in <em>standard</em> form is defined by this formula:
(1)
Where:
- Coordinates of the center of the ellipse.
,
- Lengths of each semiaxis.
Hence, the maximum distance (
), in feet, is calculated by this formula:
(2)
If we know that
, then the maximum distance between any two points of the ellipse is:


The <em>maximum</em> distance between any two points of the ellipse is 34 feet. 
<h3>Remark</h3>
The statement is incomplete and poorly formatted, correct form is presented below:
<em>An elliptical-shaped path surrounds a garden, modeled by </em>
<em>, where all measurements are in feet. What is the maximum distance between any two points of the path.</em>
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943