document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167715>Question 167715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would I complete the square for both x and y and find the equation of the circle for the given equation x^2-8x+y^2+4y-205=0. I also have the same question for the following equation x^2+12x+y^2-14y-204=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123626 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first (which hopefully will help you do the second)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2By%5E2%2B4y-205=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2By%5E2%2B4y-205=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x%2By%5E2%2B4y=%2B205 ALIGN=MIDDLE  ALT=\"x%5E2-8x%2By%5E2%2B4y=%2B205\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=205 ALIGN=MIDDLE  ALT=\"205\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2-16%2By%5E2%2B4y=205 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2-16%2By%5E2%2B4y=205\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the \"x\" terms. Note: Let me know if you need help completing the square.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2-16%2B%28y%2B2%29%5E2-4=205 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2-16%2B%28y%2B2%29%5E2-4=205\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the \"y\" terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y%2B2%29%5E2-20=205 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y%2B2%29%5E2-20=205\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y%2B2%29%5E2=205%2B20 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y%2B2%29%5E2=205%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-4%29%5E2%2B%28y%2B2%29%5E2=225 ALIGN=MIDDLE  ALT=\"%28x-4%29%5E2%2B%28y%2B2%29%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "-----------\r<BR>\n" );
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document.write( "Notice how the equation is now in the form <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;\" >. This means that this conic section is a circle where (h,k) is the center and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius.\r<BR>\n" );
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document.write( "So the circle has these properties:\r<BR>\n" );
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document.write( "Center: (4,-2)\r<BR>\n" );
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document.write( "Radius: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28225%29=15 ALIGN=MIDDLE  ALT=\"r=sqrt%28225%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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