document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008532>Question 1008532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the equation represents a circle, a point, or has no graph. If the equation is that of a circle, find its center and radius. \r<BR>\n" );
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document.write( "(2x^2)+(2y^2)-2x+8y=1/2\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #624181 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=624181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula of the circle 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( "    where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinates of the center of the circle \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B2y%5E2-2x%2B8y=1%2F2+ ALIGN=MIDDLE  ALT=\"2x%5E2%2B2y%5E2-2x%2B8y=1%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=x%5E2%2By%5E2-x%2B4y=1%2F4+ ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-x%2B4y=1%2F4+\"   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-x%29%2B%28y%5E2%2B4y%29=1%2F4+ ALIGN=MIDDLE  ALT=\"%28x%5E2-x%29%2B%28y%5E2%2B4y%29=1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >......complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x%2Bb%5E2%29-b%5E2%2B%28y%5E2%2B4y%2Bb%5E2%29-b%5E2=1%2F4+ ALIGN=MIDDLE  ALT=\"%28x%5E2-x%2Bb%5E2%29-b%5E2%2B%28y%5E2%2B4y%2Bb%5E2%29-b%5E2=1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >....recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B-b%29%5E2 ALIGN=MIDDLE  ALT=\"%28a%2B-b%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2ab%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-2ab%2Bb%5E2\"   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-x%2Bb%5E2%29-b%5E2%2B%28y%5E2%2B4y%2Bb%5E2%29-b%5E2=1%2F4+ ALIGN=MIDDLE  ALT=\"%28x%5E2-x%2Bb%5E2%29-b%5E2%2B%28y%5E2%2B4y%2Bb%5E2%29-b%5E2=1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...so, in your case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=1 ALIGN=MIDDLE  ALT=\"2ab=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <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, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=4 ALIGN=MIDDLE  ALT=\"2ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <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\r<BR>\n" );
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document.write( "then,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=1 ALIGN=MIDDLE  ALT=\"2ab=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=1 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1%2F2 ALIGN=MIDDLE  ALT=\"b=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <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\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=4 ALIGN=MIDDLE  ALT=\"2ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A1%2Ab=4 ALIGN=MIDDLE  ALT=\"2%2A1%2Ab=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4%2F2 ALIGN=MIDDLE  ALT=\"b=4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <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;\" > in <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\r<BR>\n" );
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document.write( "so, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x%2B%281%2F2%29%5E2%29-%281%2F2%29%5E2%2B%28y%5E2%2B4y%2B2%5E2%29-2%5E2=1%2F4+ ALIGN=MIDDLE  ALT=\"%28x%5E2-x%2B%281%2F2%29%5E2%29-%281%2F2%29%5E2%2B%28y%5E2%2B4y%2B2%5E2%29-2%5E2=1%2F4+\"   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%2F2%29%5E2-%281%2F4%29%2B%28y%2B2%29%5E2-4=1%2F4+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2-%281%2F4%29%2B%28y%2B2%29%5E2-4=1%2F4+\"   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%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F4%2B%281%2F4%29%2B4+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F4%2B%281%2F4%29%2B4+\"   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%2F2%29%5E2%2B%28y%2B2%29%5E2=2%2F4%2B4+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2%2B%28y%2B2%29%5E2=2%2F4%2B4+\"   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%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F2%2B4+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F2%2B4+\"   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%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F2%2B8%2F2+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2%2B%28y%2B2%29%5E2=1%2F2%2B8%2F2+\"   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%2F2%29%5E2%2B%28y%2B2%29%5E2=9%2F2+ ALIGN=MIDDLE  ALT=\"%28x-1%2F2%29%5E2%2B%28y%2B2%29%5E2=9%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, it is a circle and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=1%2F2 ALIGN=MIDDLE  ALT=\"h=1%2F2\"   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=r=sqrt%289%2F2%29=sqrt%289%29%2Fsqrt%282%29=3%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"r=sqrt%289%2F2%29=sqrt%289%29%2Fsqrt%282%29=3%2Fsqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the center is at:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=3%2Fsqrt%282%29 ALIGN=MIDDLE  ALT=\"r=3%2Fsqrt%282%29\"   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=drawing%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0Acircle%281%2F2%2C-2%2C.03%29%2Clocate%281%2F2%2C-2%2CC%281%2F2%2C-2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-5%2C+5%2C+-5%2C+5%2C-sqrt%28-%28x-1%2F2%29%5E2%2B9%2F2%29-2+%2Csqrt%28-%28x-1%2F2%29%5E2%2B9%2F2%29-2%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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