|
Question 1102048: A racetrack is in the shape of an ellipse 270 feet long and 50 feet wide. What is the width 10 feet from a vertex?
Answer by ikleyn(52801)   (Show Source):
You can put this solution on YOUR website! .
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.
--------------
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.
|
|
|
| |
