document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=105703>Question 105703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the center and the radius of the circle give by \r<BR>\n" );
document.write( "\n" );
document.write( "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 #76967 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=76967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a circle centered at (h,k) with radius, R, is given by:<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%5E2-2hx%2Bh%5E2%29%2B%28y%5E2-2ky%2Bk%5E2%29=R%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2-2hx%2Bh%5E2%29%2B%28y%5E2-2ky%2Bk%5E2%29=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%5E2-2hx%29%2B%28y%5E2-2ky%29=R%5E2-h%5E2-k%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2-2hx%29%2B%28y%5E2-2ky%29=R%5E2-h%5E2-k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's look at your equation and compare terms.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B8x%29%2B%28y%5E2%2B6y%29-24=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8x%29%2B%28y%5E2%2B6y%29-24=0\"   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%2B8x%29%2B%28y%5E2%2B6y%29=24 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8x%29%2B%28y%5E2%2B6y%29=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2hx=8x ALIGN=MIDDLE  ALT=\"-2hx=8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2ky=6y ALIGN=MIDDLE  ALT=\"-2ky=6y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-h%5E2-k%5E2=24 ALIGN=MIDDLE  ALT=\"R%5E2-h%5E2-k%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2hx=8x ALIGN=MIDDLE  ALT=\"-2hx=8x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-4 ALIGN=MIDDLE  ALT=\"h=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "From 2, <BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2ky=6y ALIGN=MIDDLE  ALT=\"-2ky=6y\"   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( "From 3,<BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-h%5E2-k%5E2=24 ALIGN=MIDDLE  ALT=\"R%5E2-h%5E2-k%5E2=24\"   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-%28-4%29%5E2-%28-3%29%5E2=24 ALIGN=MIDDLE  ALT=\"R%5E2-%28-4%29%5E2-%28-3%29%5E2=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-16-9=24 ALIGN=MIDDLE  ALT=\"R%5E2-16-9=24\"   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=49 ALIGN=MIDDLE  ALT=\"R%5E2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=7 ALIGN=MIDDLE  ALT=\"R=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Putting those values back in the first equation, <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-%28-4%29%29%5E2%2B%28y-%28-3%29%29%5E2=49 ALIGN=MIDDLE  ALT=\"%28x-%28-4%29%29%5E2%2B%28y-%28-3%29%29%5E2=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49%29 ALIGN=MIDDLE  ALT=\"highlight%28%28x%2B4%29%5E2%2B%28y%2B3%29%5E2=49%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A circle centered at (-4,-3) with a radius of 7. <BR>\n" );
document.write( "Let's verify.<BR>\n" );
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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B8x%2B16%29%2B%28y%5E2%2B6y%2B9%29=49 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B8x%2B16%29%2B%28y%5E2%2B6y%2B9%29=49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B8x%2By%5E2%2B6y%2B25-49=49-49 ALIGN=MIDDLE  ALT=\"x%5E2%2B8x%2By%5E2%2B6y%2B25-49=49-49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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;\" ><BR>\n" );
document.write( "Back to your original equation. Good answer.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );