document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144268>Question 1144268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line containing the centers of the two circles.<BR>\n" );
document.write( "X^2+y^2+6x+4y+12=0<BR>\n" );
document.write( "X^2+y^2-2x+10y+22=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765336 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The general equation of a circle with center (h,k) and radius r is<br><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><BR>\n" );
document.write( "In expanded form, that is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2hx%2Bh%5E2%2By%5E2-2ky%2Bk%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-2hx%2Bh%5E2%2By%5E2-2ky%2Bk%5E2+=+r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the problem requires us only to find the centers of the circles, we don't have to do the complete process of completing the square in x and y.  We can determine the center (h,k) of each circle from the equations in the given form.<br><BR>\n" );
document.write( "First circle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x+=+x%5E2-2hx ALIGN=MIDDLE  ALT=\"x%5E2%2B6x+=+x%5E2-2hx\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> h = -3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B4y+=+y%5E2-2ky ALIGN=MIDDLE  ALT=\"y%5E2%2B4y+=+y%5E2-2ky\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> k = -2<BR>\n" );
document.write( "The center of the circle is (-3,-2)<br><BR>\n" );
document.write( "Second circle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x+=+x%5E2-2hx ALIGN=MIDDLE  ALT=\"x%5E2-2x+=+x%5E2-2hx\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> h = __<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B10y+=+y%5E2-2ky ALIGN=MIDDLE  ALT=\"y%5E2%2B10y+=+y%5E2-2ky\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> k = __<br><BR>\n" );
document.write( "I will assume you then know at least one way to find an equation of the line containing those two centers.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );