document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=865420>Question 865420</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A hall 100 feet in length is to be designed as  a whispering gallery ( a hall with elliptical ceiling). If the foci are located 25 feet from the center, how high will the ceiling be at center?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521688 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521688\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A hall 100 feet in length is to be designed as a whispering gallery ( a hall with elliptical ceiling). If the foci are located 25 feet from the center, how high will the ceiling be at center?<BR>\n" );
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document.write( "standard form of equation for an ellipse with horizontal major axis and center at the origin:<BR>\n" );
document.write( "x^2/a^2+y^2/b^2=1, a>b<BR>\n" );
document.write( "for given problem:<BR>\n" );
document.write( "a=50<BR>\n" );
document.write( "a^2=2500<BR>\n" );
document.write( "c=25<BR>\n" );
document.write( "c^2=625<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=2500-625=1875<BR>\n" );
document.write( "b=&#8730;1875&#8776;43.3 ft<BR>\n" );
document.write( "how high will the ceiling be at center? &#8776;43.3 ft above center<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );