Question 1140779
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<pre>
Each of the two focuses of an ellipse is located on its major axis at the distance of  c = {{{sqet(a^2 - b^2)}}} from its center,


where "a" is the major semi-axis of the ellipse and "b" is its minor semi-axis.



In the given case,  a = {{{92/2}}} = 46 ft,  b = {{{58/2}}} = 29 ft,  so


the distance from the center of the ellipse to any of the two its focuses is


    c = {{{sqrt(46^2 - 29^2)}}} = 35.707 ft.


The distance between the focuses is two times this value, i.e.  2*35.707 = 71.14 ft.     <U>ANSWER</U>
</pre>

Solved.


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For this and other remarkable properties of ellipses 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=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Ellipse-focal-property.lesson>Ellipse focal property</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Tangen-lines-to-a-circle.lesson>Tangent lines and normal vectors to a circle</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Tangent-lines-to-an-ellipse.lesson>Tangent lines and normal vectors to an ellipse</A> 

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Optical-property-of-an-ellipse-revisited.lesson>Optical property of an ellipse revisited</A> 

in this site.