document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=723537>Question 723537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the graph of the equation below is an ellipse. How long is the major axis of the ellipse given by the equation? (x+7)^2 5^2 + (y-4)^2 8^2= 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #443212 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=443212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the equation is really <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E2+%2A5%5E2+%2B+%28y-4%29%5E2%2A+8%5E2=+1 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E2+%2A5%5E2+%2B+%28y-4%29%5E2%2A+8%5E2=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > the major and minor axes are not very long.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-8%2C1%2C-2%2C8%2C25%28x%2B7%29%5E2%2B64%28y-4%29%5E2%3C=1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-8%2C1%2C-2%2C8%2C25%28x%2B7%29%5E2%2B64%28y-4%29%5E2%3C=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > the second term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-4%29%5E2%2A+8%5E2=0%5E2%2A+8%5E2=0%2A+8%5E2=0 ALIGN=MIDDLE  ALT=\"%284-4%29%5E2%2A+8%5E2=0%5E2%2A+8%5E2=0%2A+8%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and you get the extreme values for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E2+%2A5%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E2+%2A5%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E2+=+1%2F5%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E2+=+1%2F5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7=-1%2F5 ALIGN=MIDDLE  ALT=\"x%2B7=-1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7=1%2F5 ALIGN=MIDDLE  ALT=\"x%2B7=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which can be summarized as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7+%2B-+1%2F5 ALIGN=MIDDLE  ALT=\"x=-7+%2B-+1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the horizontal axis would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5 ALIGN=MIDDLE  ALT=\"2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > in length, the distance between those two extreme points. That is the major axis, the longest one.<BR>\n" );
document.write( "The ends of the shorter vertical axis can be found for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4+%2B-+1%2F8 ALIGN=MIDDLE  ALT=\"y=4+%2B-+1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which makes the length of that axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%281%2F8%29=1%2F4 ALIGN=MIDDLE  ALT=\"2%281%2F8%29=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the equation was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%5E2%2F5%5E2+%2B+%28y-4%29%5E2%2F8%5E2=+1 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%5E2%2F5%5E2+%2B+%28y-4%29%5E2%2F8%5E2=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > instead,<BR>\n" );
document.write( "the ends of the horizontal axis would still be at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4 ALIGN=MIDDLE  ALT=\"y=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7+%2B-+5 ALIGN=MIDDLE  ALT=\"x=-7+%2B-+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the ends of the vertical axis would still be at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=4+%2B-+8 ALIGN=MIDDLE  ALT=\"y=4+%2B-+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The length of the axes would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A5=10 ALIGN=MIDDLE  ALT=\"2%2A5=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the shorter, horizontal, minor axis,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A8=16 ALIGN=MIDDLE  ALT=\"2%2A8=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the longer, vertical, major axis.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-16%2C4%2C-6%2C14%2C%28x%2B7%29%5E2%2F25%2B%28y-4%29%5E2%2F64%3C=1%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-16%2C4%2C-6%2C14%2C%28x%2B7%29%5E2%2F25%2B%28y-4%29%5E2%2F64%3C=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );