document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206482>Question 1206482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the two circles defined by the equations x^(2)-6x+y^(2)+8y=12 and x^(2)+y^(2)=4y, find the algebraic equation of the line connecting their centers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844004 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=844004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "If you need to find the centers and radii of the two circles, then you need to complete the squares.<br><BR>\n" );
document.write( "In this problem, you are to find the equation of the line connecting the centers of the circles.  That means you don't need to know the radii of the two circles; and that means completing the square is unnecessary work.<br><BR>\n" );
document.write( "As tutor @ikleyn says, you can find the centers of the two circles mentally:<br><BR>\n" );
document.write( "First circle: (x^2-6x+...)+(y^2+8y+...) = ... ---> center (3,-4)<BR>\n" );
document.write( "Second circle: (x^2)+(y^2-4y+...) = ... ---> center (0,2)<br><BR>\n" );
document.write( "Then finding the equation of the line containing those two centers is a basic algebraic process.<br><BR>\n" );
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