Question 1102048
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<pre>
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  {{{270/2}}} = 135 ft long  and the minor semi-axis is  {{{50/2}}} = 25 ft long.


Then the equation of the ellipse is

{{{x^2/135^2 + y^2/25^2}}} = 1.


Hence,  y = +/- {{{25*sqrt(1 - x^2/135^2)}}}.


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

{{{y[1,2]}}} = +/- {{{25*sqrt(1-(125/135)^2)}}} = +/- 9.443 (approximately . . . )


Thus the distance between these two points is 2*9.443 = 18.886 ft.


<U>Answer</U>.  At the requested distance from the vertex, the width of the ellipse is 18.886 ft.
</pre>


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On equations for ellipses that might be useful to you, see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-definition--canonical-equation--characteristic-points-and-elements.lesson>Ellipse definition, canonical equation, characteristic points and elements</A> 


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-an-ellipse.lesson>Standard equation of an ellipse</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-an-ellipse-given-by-its-standard-eqn.lesson>Identify elements of an ellipse given by its standard equation</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-a-standard-equation-of-an-ellipse-given-by-its-elements.lesson>Find the standard equation of an ellipse given by its elements</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/General-equation-of-an-ellipse.lesson>General equation of an ellipse</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Transform-general-eqn-of-an-ellipse-to-the-standard-form-by-completing-the-square.lesson>Transform a general equation of an ellipse to the standard form by completing the square</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-vertices-co-vertices-foci-of-the-ellipse-given-by-an-equation.lesson>Identify elements of an ellipse given by its general equation</A>


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>".



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.