document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207523>Question 1207523</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that 2x ^ 2 + 3y^2 - x + 2y + 1 = 0 is a circle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845446 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=845446\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "a circle formula is\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+%2B%28y-k%29%5E2=r%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2+%2B%28y-k%29%5E2=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, complete squares in given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+3y%5E2+-+x+%2B+2y+%2B+1+=0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+3y%5E2+-+x+%2B+2y+%2B+1+=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=%282x%5E2-x%29+%2B+%283y%5E2+%2B+2y%29++=-1 ALIGN=MIDDLE  ALT=\"%282x%5E2-x%29+%2B+%283y%5E2+%2B+2y%29++=-1\"   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=2%28x%5E2-x%2F2%29%2B3%28y%5E2%2B2y%2F3%29=-1 ALIGN=MIDDLE  ALT=\"2%28x%5E2-x%2F2%29%2B3%28y%5E2%2B2y%2F3%29=-1\"   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=2%28x%5E2-%281%2F2%29x%2Bb%5E2%29-2b%5E2%2B3%28y%5E2%2B%282%2F3%29y%2Bb%5E2%29-3b%5E2=-1 ALIGN=MIDDLE  ALT=\"2%28x%5E2-%281%2F2%29x%2Bb%5E2%29-2b%5E2%2B3%28y%5E2%2B%282%2F3%29y%2Bb%5E2%29-3b%5E2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%281%2F2%29%2F2=1%2F4 ALIGN=MIDDLE  ALT=\"b=%281%2F2%29%2F2=1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%282%2F3%29%2F2=1%2F3 ALIGN=MIDDLE  ALT=\"b=%282%2F3%29%2F2=1%2F3\"   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=2%28x%5E2-%281%2F2%29x%2B%281%2F4%29%5E2%29-2%281%2F4%29%5E2%2B3%28y%5E2%2B%282%2F3%29y%2B%281%2F3%29%5E2%29-3%281%2F3%29%5E2=-1 ALIGN=MIDDLE   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=2%28x-1%2F4%29%5E2-2%281%2F16%29%2B3%28y%2B1%2F3%29%5E2-3%281%2F9%29=-1 ALIGN=MIDDLE  ALT=\"2%28x-1%2F4%29%5E2-2%281%2F16%29%2B3%28y%2B1%2F3%29%5E2-3%281%2F9%29=-1\"   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=2%28x-1%2F4%29%5E2-1%2F8%2B3%28y%2B1%2F3%29%5E2-1%2F3=-1 ALIGN=MIDDLE  ALT=\"2%28x-1%2F4%29%5E2-1%2F8%2B3%28y%2B1%2F3%29%5E2-1%2F3=-1\"   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=2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-1%2B1%2F8%2B1%2F3 ALIGN=MIDDLE  ALT=\"2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-1%2B1%2F8%2B1%2F3\"   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=2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-13%2F24 ALIGN=MIDDLE  ALT=\"2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-13%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "as you can see, we cannot get a formula of a circle which means given equation is NOT a circle\r<BR>\n" );
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