document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183194>Question 183194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given that the equation of a circle is x^2+y^2-10x+4y+13=0, find its center and its radius. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137551 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=137551\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-10x%2B4y%2B13=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-10x%2B4y%2B13=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%2By%5E2-10x%2B4y=-13 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-10x%2B4y=-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 13 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%29%2B%28y%5E2%2B4y%29=-13 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%29%2B%28y%5E2%2B4y%29=-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-10x%2Bhighlight%2825%29%29%2B%28y%5E2%2B4y%29=-13%2Bhighlight%2825%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2Bhighlight%2825%29%29%2B%28y%5E2%2B4y%29=-13%2Bhighlight%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the \"x\" coefficient -10 to get -5. Square it to get 25. Add this 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%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2Bhighlight%284%29%29=-13%2B25%2Bhighlight%284%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2Bhighlight%284%29%29=-13%2B25%2Bhighlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take half of the \"y\" coefficient 4 to get 2. Square that result to get 4. Add this 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%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=-13%2B25%2B4 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=-13%2B25%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%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=16 ALIGN=MIDDLE  ALT=\"%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=16\"   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-5%29%5E2%2B%28y%5E2%2B4y%2B4%29=16 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%5E2%2B4y%2B4%29=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-10x%2B25 ALIGN=MIDDLE  ALT=\"x%5E2-10x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%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-5%29%5E2%2B%28y%2B2%29%5E2=16 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%2B2%29%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B4y%2B4 ALIGN=MIDDLE  ALT=\"y%5E2%2B4y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%2B2%29%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-5%29%5E2%2B%28y%2B2%29%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y%2B2%29%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2 ALIGN=MIDDLE  ALT=\"4%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-5%29%5E2%2B%28y-%28-2%29%29%5E2=4%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2%2B%28y-%28-2%29%29%5E2=4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2B2 ALIGN=MIDDLE  ALT=\"y%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-%28-2%29 ALIGN=MIDDLE  ALT=\"y-%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So 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;\" > (which is a circle) where (h,k) is the center and \"r\" is the radius\r<BR>\n" );
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document.write( "We can see that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=5 ALIGN=MIDDLE  ALT=\"h=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the center is (5,-2) and the radius is 4 units </SPAN>\n" );
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