document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=455942>Question 455942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the center, vertices, co-vertices, and foci of this ellipse x squared+4y squared-2x+16y+13=0? I tried subtracting 13 to both sides then factoring everything else but it doesn't look right. Can someone help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #312991 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=312991\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Rational Exponents\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4y%5E2-2x%2B16y%2B13=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4y%5E2-2x%2B16y%2B13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-2x%29%2B%284y%5E2%2B16y%29%2B13=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%29%2B%284y%5E2%2B16y%29%2B13=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B16-4 ALIGN=MIDDLE  ALT=\"1%2B16-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-2x%2B1%29%2B%284y%5E2%2B16y%2B16%29+-4=0 ALIGN=MIDDLE  ALT=\"%28x%5E2-2x%2B1%29%2B%284y%5E2%2B16y%2B16%29+-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2B4+%28y%2B2%29%5E2-4+=+0 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2B4+%28y%2B2%29%5E2-4+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2B4+%28y%2B2%29%5E2=4+ ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2B4+%28y%2B2%29%5E2=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F4%29+%28x-1%29%5E2%2B%28y%2B2%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%281%2F4%29+%28x-1%29%5E2%2B%28y%2B2%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%5E2%2F4%2B%28y%2B2%29%5E2%2F1+=+1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2%2F4%2B%28y%2B2%29%5E2%2F1+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >....compare to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...if the major axis runs horizontally\r<BR>\n" );
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document.write( "you see that:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1 ALIGN=MIDDLE  ALT=\"h=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-2 ALIGN=MIDDLE  ALT=\"k=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The center of the ellipse is (h,k) = (1,-2).<BR>\n" );
document.write( "The major vertices are (h-a,k) and (h+a,k)  or (-1,-2) and (3,-2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+sqrt%28a%5E2+-+b%5E2%29+=sqrt%284+-+1%29+=+sqrt%283%29+=+1.73 ALIGN=MIDDLE  ALT=\"c+=+sqrt%28a%5E2+-+b%5E2%29+=sqrt%284+-+1%29+=+sqrt%283%29+=+1.73\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The foci are (h-c,k) and (h+c,k) or<BR>\n" );
document.write( "(1-1.73,-2) and (1+1.73,-2) which is (-0.73,-2) and (2.73,-2).<BR>\n" );
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