document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=462331>Question 462331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the foci of the ellipse given by the equation [((x-2)^2)/36]+[((y-8)^2)/144]=1?\r<BR>\n" );
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document.write( "Please explain! I am having trouble with this. \r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #316949 by </B><A HREF=/tutors/aboutme.mpl?userid=graphmatics><B>graphmatics(170)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=graphmatics><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/cgi-bin/show-face.mpl?user=graphmatics><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=316949\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ((x-2)^2)/36+((y-8)^2)/144=1\r<BR>\n" );
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document.write( "From the general equation<BR>\n" );
document.write( "[((x-h)^2)/a^2]+[((y-k)^2)/b^2]=1 we know that the center of the ellipse is at  (h,k). So for our ellipse equation the center of the ellipse is at (2,8).\r<BR>\n" );
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document.write( "c is the distance from the center to a focus point. The expression for c (when b > a) is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28+b%5E2-a%5E2+%29+ ALIGN=MIDDLE  ALT=\"c+=+sqrt%28+b%5E2-a%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So for our ellipse<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28+12%5E2-6%5E2+%29+ ALIGN=MIDDLE  ALT=\"c+=+sqrt%28+12%5E2-6%5E2+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28+144-36+%29+ ALIGN=MIDDLE  ALT=\"c+=+sqrt%28+144-36+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28+108+%29+ ALIGN=MIDDLE  ALT=\"c+=+sqrt%28+108+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+10.3923+ ALIGN=MIDDLE  ALT=\"c+=+10.3923+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The expression for the foci of a general ellipse is<BR>\n" );
document.write( "Foci: (c+h, k) (-c+h, k)<BR>\n" );
document.write( "So for our ellipse the foci are (10.3923+2, 8) (-10.3923+2, 8)<BR>\n" );
document.write( "(12.3923, 8) (-8.3923, 8)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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