document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=14354>Question 14354</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the line (in either general form or slope intercept form) that contains the centers of the following two circles:\r<BR>\n" );
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document.write( "x^2+y^2-4x+6y+4 = 0     and        x^2+y^2+6x+4y+9 = 0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #7452 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=7452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation of a circle with centre as (h,k) and radius r is given by the formula<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( "  So we have to write the given equation in this form to get the centre of the circle.<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2-4%2Ax%2B6%2Ay%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-4%2Ax%2B6%2Ay%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4%2Ax%2By%5E2%2B6%2Ay%2B4=0 ALIGN=MIDDLE  ALT=\"x%5E2-4%2Ax%2By%5E2%2B6%2Ay%2B4=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-2%29%5E2-4%2B%28y%2B3%29%5E2-9%2B4=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2-4%2B%28y%2B3%29%5E2-9%2B4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...Note that we have added and subtracted 4 and 9 to make up the squares mentioned in brackets.<BR>\n" );
document.write( " Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%5E2%2B%28y%2B3%29%5E2=9 ALIGN=MIDDLE  ALT=\"%28x-2%29%5E2%2B%28y%2B3%29%5E2=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Hence (2,-3)is the centre of this circle .Similarly the centre of the second circle is obtained from <BR>\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6%2Ax%2B4%2Ay%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6%2Ax%2B4%2Ay%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6%2Ax%2By%5E2%2B4%2Ay%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6%2Ax%2By%5E2%2B4%2Ay%2B9=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%2B3%29%5E2-9%2B%28y%2B2%29%5E2-4%2B9=0 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2-9%2B%28y%2B2%29%5E2-4%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...Note that we have added and subtracted 9 and 4 to make up the squares mentioned in brackets.<BR>\n" );
document.write( " Hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2%2B%28y%2B2%29%5E2=4 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2%2B%28y%2B2%29%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Hence the centre of the second circle is (-3,-2)<BR>\n" );
document.write( "  The equation of line joining 2 ponts  (x1,y1) and (x2,y2)is given by the formula <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y-y1=%28y2-y1%29%2A%28X-x1%29%2F%28%28x2-x1%29%29 ALIGN=MIDDLE  ALT=\"Y-y1=%28y2-y1%29%2A%28X-x1%29%2F%28%28x2-x1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " Substituting (2,-3) and (-3,-2) in the above formula we get <BR>\n" );
document.write( " Y-(-3)=(-2-(-3))*(X-2)/(-3-(-2))<BR>\n" );
document.write( "  Y+3=(X-2)/(-5)<BR>\n" );
document.write( "-5Y-15=X-2<BR>\n" );
document.write( "X+5Y+13=0\r<BR>\n" );
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