document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=140867>Question 140867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tutors can you help me?*\r<BR>\n" );
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document.write( "find the center and the radius of the circle given by x^2+8x+y^2+6y-24=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #102504 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=102504\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2By%5E2%2B6y-24=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2By%5E2%2B6y-24=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%2B8x%2By%5E2%2B6y=%2B24 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2By%5E2%2B6y=%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   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%2B4%29%5E2-16%2By%5E2%2B6y=%2B24 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2-16%2By%5E2%2B6y=%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Complete the square for the x terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2-16%2B%28y%2B3%29%5E2-9=%2B24 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2-16%2B%28y%2B3%29%5E2-9=%2B24\"   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%2B4%29%5E2%2B%28y%2B3%29%5E2-25=%2B24 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y%2B3%29%5E2-25=%2B24\"   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%2B4%29%5E2%2B%28y%2B3%29%5E2=%2B24%2B25 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=%2B24%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   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%2B4%29%5E2%2B%28y%2B3%29%5E2=49 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\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,-3)\r<BR>\n" );
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document.write( "Radius: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%2849%29=7 ALIGN=MIDDLE  ALT=\"r=sqrt%2849%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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