document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126420>Question 126420</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> i really need help with this problem i tried it but it didnt work out. it says an ellipse with center at the origin and horizontal major axis is to fit snugly inside a rectangle that has its longer sides horizontal. the area of the rectangle is 12 square units, and the perimeter is 14 units. find an equation for the ellipse.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92621 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=92621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> an ellipse with center at the origin and horizontal major axis is to fit snugly inside a rectangle that has its longer sides horizontal. the area of the rectangle is 12 square units, and the perimeter is 14 units. find an equation for the ellipse. <BR>\n" );
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document.write( "Find the length and width of the rectangle:<BR>\n" );
document.write( "2(length + width) = 14<BR>\n" );
document.write( "l + w = 7<BR>\n" );
document.write( "lw = 12<BR>\n" );
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document.write( "l=7-w<BR>\n" );
document.write( "(7-w)w = 12<BR>\n" );
document.write( "-w^2+7w=12<BR>\n" );
document.write( "w^2-7w+12=0<BR>\n" );
document.write( "(w-3)(w-4) = 0<BR>\n" );
document.write( "w = 3, then length = 4<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "w = 4, then length = 3<BR>\n" );
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document.write( "The longer side is horizontal so must be 4.<BR>\n" );
document.write( "The shorter side must be 3.<BR>\n" );
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document.write( "The semi-major axis must be 2.<BR>\n" );
document.write( "The semi-minor axis must be 1.5<BR>\n" );
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document.write( "Equation of the ellipse:<BR>\n" );
document.write( "x^2/2^2 + y^2/1.5^2 = 1<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );