document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856394>Question 856394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center,foci, vertices and lengh\th of the axes for the ellipse<BR>\n" );
document.write( " Equation:4x^2+y^2+24x-10y+45=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515931 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=515931\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2By%5E2%2B24x-10y%2B45=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2By%5E2%2B24x-10y%2B45=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2By%5E2-10y=-45 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2By%5E2-10y=-45\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2B36%2By%5E2-10y%2B25=-45%2B36%2B25 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B36%2By%5E2-10y%2B25=-45%2B36%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2%2B6x%2B9%29%2B%28y-5%29%5E2=16 ALIGN=MIDDLE  ALT=\"4%28x%5E2%2B6x%2B9%29%2B%28y-5%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B3%29%5E2%2B%28y-5%29%5E2=16 ALIGN=MIDDLE  ALT=\"4%28x%2B3%29%5E2%2B%28y-5%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B3%29%5E2%2F16%2B%28y-5%29%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"4%28x%2B3%29%5E2%2F16%2B%28y-5%29%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2F4%2B%28y-5%29%5E2%2F16=1 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2F4%2B%28y-5%29%5E2%2F16=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2F2%5E2%2B%28y-5%29%5E2%2F4%5E2=1 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2F2%5E2%2B%28y-5%29%5E2%2F4%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the equation of an ellipse<BR>\n" );
document.write( "centered at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28+-3+%2C+5+%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28+-3+%2C+5+%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with major axis parallel to the y-axis<BR>\n" );
document.write( "and semi-major axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with minor axis parallel to the x-axis<BR>\n" );
document.write( "and semi-major axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and a focal distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > such that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2%2Bc%5E2=a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2%2Bc%5E2=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2%2Bc%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"2%5E2%2Bc%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Bc%5E2=16 ALIGN=MIDDLE  ALT=\"4%2Bc%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=16-4 ALIGN=MIDDLE  ALT=\"c%5E2=16-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5E2=12 ALIGN=MIDDLE  ALT=\"c%5E2=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=sqrt%2812%29 ALIGN=MIDDLE  ALT=\"c=sqrt%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"c=2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=about3.464 ALIGN=MIDDLE  ALT=\"c=about3.464\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-7%2C3%2C-1%2C10%2C%0D%0Agrid%281%29%2Cred%28circle%28-3%2C5%2C0.1%29%29%2C%0D%0Ared%28arc%28-3%2C5%2C4%2C8%2C0%2C360%29%29%2C%0D%0Ared%28circle%28-3%2C9%2C0.1%29%29%2C%0D%0Ared%28circle%28-3%2C1%2C0.1%29%29%2C%0D%0Agreen%28circle%28-3%2C8.464%2C0.1%29%29%2C%0D%0Agreen%28circle%28-3%2C1.536%2C0.1%29%29%2C%0D%0Alocate%28-6.5%2C9.6%2Cred%28vertex%29%29%2C%0D%0Alocate%28-6.5%2C0.9%2Cred%28vertex%29%29%2C%0D%0Alocate%28-4.6%2C5.5%2Cred%28center%29%29%2C%0D%0Alocate%28-4.6%2C1.9%2Cgreen%28focus%29%29%2C%0D%0Alocate%28-4.6%2C8.9%2Cgreen%28focus%29%29%2C%0D%0Ared%28arrow%28-4.8%2C9.3%2C-3.15%2C9.1%29%29%2C%0D%0Ared%28arrow%28-4.8%2C0.6%2C-3.15%2C0.9%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertices are 4 units above and 4 units below the center,<BR>\n" );
document.write( "at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28+-3+%2C+9+%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28+-3+%2C+9+%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28+-3+%2C+1+%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28+-3+%2C+1+%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The foci are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > above and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29 ALIGN=MIDDLE  ALT=\"2sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > below the center,<BR>\n" );
document.write( "at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28+-3+%2C+5%2B2+sqrt%283%29%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28+-3+%2C+5%2B2+sqrt%283%29%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%22%28+-3+%2C+5-2+sqrt%283%29%29%22%29 ALIGN=MIDDLE  ALT=\"highlight%28%22%28+-3+%2C+5-2+sqrt%283%29%29%22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The length of the major axis is the distance between the vertices<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a=2%2A4=highlight%288%29 ALIGN=MIDDLE  ALT=\"2a=2%2A4=highlight%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The length of the minor axis is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=2%2A2=highlight%284%29 ALIGN=MIDDLE  ALT=\"2b=2%2A2=highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );