.
According to the condition, the ellipse has the major axis of the length 270 ft and the minor axis of the length 50 ft.
Then the major semi-axis is = 135 ft long and the minor semi-axis is = 25 ft long.
Then the equation of the ellipse is
= 1.
Hence, y = +/- .
The point at 10 feet from the vertex is at x= 135-10 = 125 ft (the vertex is at x= 135 ft).
Therefore, y-coordinates for two points at the ellipse that have x-coordinate 125, are
= +/- = +/- 9.443 (approximately . . . )
Thus the distance between these two points is 2*9.443 = 18.886 ft.
Answer. At the requested distance from the vertex, the width of the ellipse is 18.886 ft.
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On equations for ellipses that might be useful to you, see the lessons
- Ellipse definition, canonical equation, characteristic points and elements
- Standard equation of an ellipse
- Identify elements of an ellipse given by its standard equation
- Find the standard equation of an ellipse given by its elements
- General equation of an ellipse
- Transform a general equation of an ellipse to the standard form by completing the square
- Identify elements of an ellipse given by its general equation
Also, you have this free of charge online textbook in ALGEBRA-II in this site
ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic
"Conic sections: Ellipses. Definition, major elements and properties. Solved problems".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.