document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=454540>Question 454540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an equation for each ellipse described below:<BR>\n" );
document.write( "the endpoints of the major axis are at (10,2) and (-8,2). The foci are at (6,2) and (-4,2).\r<BR>\n" );
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document.write( "I have found that the center is at (1,2), but this may be wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312338 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=312338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write an equation for the ellipse described below:<BR>\n" );
document.write( "the endpoints of the major axis are at (10,2) and (-8,2). The foci are at (6,2) and (-4,2). <BR>\n" );
document.write( "I have found that the center is at (1,2), but this may be wrong.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of a^2 and b^2.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Major axis and foci located on the line, y=2, shows that this ellipse has a horizontal major axis, with center at (1,2) as you correctly figured out.<BR>\n" );
document.write( "Center (1,2)<BR>\n" );
document.write( "length of major axis=18=2a<BR>\n" );
document.write( "a=9<BR>\n" );
document.write( "a^2=81<BR>\n" );
document.write( "2c=10<BR>\n" );
document.write( "c=5<BR>\n" );
document.write( "c^2=25<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=81-25=56<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "(x-1)^2/81+(y-2)^2/56=1<BR>\n" );
document.write( "See the graph below for a visual check on the answers.<BR>\n" );
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document.write( "y=(56-56(x-1)^2/81)^.5+2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-20%2C+20%2C+-20%2C+20%2C+%2856-56%28x-1%29%5E2%2F81%29%5E.5%2B2%2C-%2856-56%28x-1%29%5E2%2F81%29%5E.5%2B2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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