document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=61071>Question 61071</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the center and the radius of the circle:<BR>\n" );
document.write( "x2 + y2 - 12x-16y-21 =0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41990 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=41990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the centre and radius of the circle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+12x+-+16y+-+21+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+12x+-+16y+-+21+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > First, add 21 to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+12x+-+16y+=+21 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+12x+-+16y+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now group the x-terms together and the y-terms together.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x%29+%2B+%28y%5E2+-+16y%29+=+21 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x%29+%2B+%28y%5E2+-+16y%29+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Next, complete the square in x by adding the square of half the x-coefficient to both sides of the equation. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%2F2%29%5E2+=+36 ALIGN=MIDDLE  ALT=\"%28-12%2F2%29%5E2+=+36\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the same for the y <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-16%2F2%29%5E2+=+64 ALIGN=MIDDLE  ALT=\"%28-16%2F2%29%5E2+=+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x+%2B+36%29+%2B+%28y%5E2+-+16y+%2B+64%29+=+21+%2B+36+%2B+64 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x+%2B+36%29+%2B+%28y%5E2+-+16y+%2B+64%29+=+21+%2B+36+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+12x+%2B+36%29+%2B+%28y%5E2+-+16y+%2B+64%29+=+121 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+12x+%2B+36%29+%2B+%28y%5E2+-+16y+%2B+64%29+=+121\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the x-group and the y-group.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29%5E2+%2B+%28y+-+8%29%5E2+=+121 ALIGN=MIDDLE  ALT=\"%28x+-+6%29%5E2+%2B+%28y+-+8%29%5E2+=+121\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Take the square root of 121 = 11<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29%5E2+%2B+%28y+-+8%29%5E2+=+%2811%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-+6%29%5E2+%2B+%28y+-+8%29%5E2+=+%2811%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Compare with the standard form for a circle with centre at (h, k) and radius, r.<BR>\n" );
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" );
document.write( "\n" );
document.write( "The circle centre is at (6, 8) and the radius is 11<BR>\n" );
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