document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=599205>Question 599205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> x^2+y^2+8x-6y=0<BR>\n" );
document.write( "find the center and radius </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #378876 by </B><A HREF=/tutors/aboutme.mpl?userid=math-vortex><B>math-vortex(648)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math-vortex><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=math-vortex><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=378876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi, there--<BR>\n" );
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document.write( "The equation for a circle has the form \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;\" ><BR>\n" );
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document.write( "The ordered pair (h,k) is the center of the circle and r is the radius. We need to transform the given equation to this form to find the center and radius.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B8x-6y=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B8x-6y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We will use the \"completing the square\" method. The polynomial x^2+8x+16 is a perfect square [(8/2)^2=16], so we need to add 16 to both sides of the equation and re-arrange the terms.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B8x%2B16%29%2By%5E2-6y=0%2B16 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8x%2B16%29%2By%5E2-6y=0%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The polynomial y^2-6y+9 is a perfect square, so we need to add 9 to both sides of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B8x%2B16%29%2B%28y%5E2-6y%2B9%29=16%2B9 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8x%2B16%29%2B%28y%5E2-6y%2B9%29=16%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now write the polynomial expressions in factored form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2B%28y-3%29%5E2=25 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y-3%29%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then write the constant term as the square of a number.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%5E2%2B%28y-3%29%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%5E2%2B%28y-3%29%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation is now in standard form, so the center=(h,k) is (-4,3), and the radius is 5.<BR>\n" );
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document.write( "That's it. Feel free to email via my gmail account if you have questions about the solution.<BR>\n" );
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document.write( "Ms.Figgy<BR>\n" );
document.write( "math.in.the.vortex@gmail.com </SPAN>\n" );
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