document.write( "Question 1088120: A whispering gallery has a semielliptical ceiling that is 12m high and 40m long how high is the ceiling above the two foci? \n" ); document.write( "

Algebra.Com's Answer #702429 by ikleyn(52813) $\"\"$ $\"About$

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document.write( "From the condition, the major semi-axis of the ellipse has the length of a = 20 m.\r\n" );
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document.write( "The length of the minor semi-axis is b = 12 m.\r\n" );
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document.write( "The linear eccentricity is c =  =  =  =  = 16.\r\n" );
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document.write( "So the foci are located on the major axis (which is the horizontal line at the floor) \r\n" );
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document.write( "at the distance of 16 m from the center point.\r\n" );
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document.write( "Taking the center point as the origin of the coordinate system,\r\n" );
document.write( "the standard equation of the ellipse is \r\n" );
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document.write( " +  = 1.              (1)\r\n" );
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document.write( "Then y = +/- .     (2)\r\n" );
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document.write( "To calculate the elevation at the focus, we must substitute x = 16 into the formula (2) and calculate y:\r\n" );
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document.write( "y =  =  =  =  = 7.2 m.\r\n" );
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document.write( "Answer.  The ceiling above the two foci is at 7.2 m.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The prerequisite for this solution is the lesson\r
\n" ); document.write( "\n" ); document.write( " - Ellipse definition, canonical equation, characteristic points and elements \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( " ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Ellipses. Definition, major elements and properties. Solved problems\".\r
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