Question 1088120
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<pre>
From the condition, the major semi-axis of the ellipse has the length of a = 20 m.

The length of the minor semi-axis is b = 12 m.

The linear eccentricity is c = {{{sqrt(a^2 - b^2)}}} = {{{sqrt(20^2-12^2)}}} = {{{sqrt(400 - 144)}}} = {{{sqrt(256)}}} = 16.


So the foci are located on the major axis (which is the horizontal line at the floor) 

at the distance of 16 m from the center point.


Taking the center point as the origin of the coordinate system,
the standard equation of the ellipse is 

{{{x^2/400}}} + {{{y^2/144}}} = 1.              (1)


Then y = +/- {{{12*sqrt(1-x^2/400)}}}.     (2)


To calculate the elevation at the focus, we must substitute x = 16 into the formula (2) and calculate y:

y = {{{12*sqrt(1-16^2/400)}}} = {{{12*sqrt(144/400)}}} = {{{(12*12)/20}}} = {{{36/5}}} = 7.2 m.


<U>Answer</U>.  The ceiling above the two foci is at 7.2 m.
</pre>

Solved.


The prerequisite for this solution is the lesson

&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> 

in this site.


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>".