document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126884>Question 126884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please help me solve this? find the center (h,k) and radius r of the circle. I have no idea how to work out.<BR>\n" );
document.write( "x^2+y^2-12x+6y+35=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #92943 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=92943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Start with the general formula for a circle<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;\" ><BR>\n" );
document.write( "Somehow you have to get your equation into that form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2+-+12x+%2B+6y+%2B+35+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2+-+12x+%2B+6y+%2B+35+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Group the x terms together and the y terms together<BR>\n" );
document.write( "and subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35 ALIGN=MIDDLE  ALT=\"35\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+y%5E2+%2B+6y+=+-35 ALIGN=MIDDLE  ALT=\"x%5E2+-+12x+%2B+y%5E2+%2B+6y+=+-35\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now do the operation called completing the square<BR>\n" );
document.write( "on the x terms and the y terms<BR>\n" );
document.write( "You do that by taking 1/2 of the coefficient of <BR>\n" );
document.write( "x (or y), squaring it, then add it to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+%2812%2F2%29%5E2+%2B+y%5E2+%2B+6y+%2B+%286%2F2%29%5E2+=+-35+%2B+%2812%2F2%29%5E2+%2B+%286%2F2%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Notice that this is the exact same equation<BR>\n" );
document.write( "I started with because I added the same thing to BOTH sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+12x+%2B+36+%2B+y%5E2+%2B+6y+%2B+9+=+-35+%2B+36+%2B+9 ALIGN=MIDDLE  ALT=\"x%5E2+-+12x+%2B+36+%2B+y%5E2+%2B+6y+%2B+9+=+-35+%2B+36+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now you can get this into the form<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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29%5E2+%2B+%28y+%2B+3%29%5E2+=+10 ALIGN=MIDDLE  ALT=\"%28x+-+6%29%5E2+%2B+%28y+%2B+3%29%5E2+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If you just match up the terms, you see that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+6 ALIGN=MIDDLE  ALT=\"h+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-3 ALIGN=MIDDLE  ALT=\"k+=+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+10 ALIGN=MIDDLE  ALT=\"r%5E2+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+sqrt%2810%29 ALIGN=MIDDLE  ALT=\"r+=+sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the center is at (6,-3) and the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );