document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=989022>Question 989022</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equations of the two circles with centres on the x-axis and radius 4 which both touch the circle x^2 + y^2- 2x-6y+ 9= 0 externally </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612821 by </B><A HREF=/tutors/aboutme.mpl?userid=anand429><B>anand429(138)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=anand429><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=anand429><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=612821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+y%5E2-+2x-6y%2B+9=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+y%5E2-+2x-6y%2B+9=+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-1%29%5E2+%2B+%28y-3%29%5E2+=+1 ALIGN=MIDDLE  ALT=\"%28x-1%29%5E2+%2B+%28y-3%29%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, centre of given circle, is (1,3) and radius 1.\r<BR>\n" );
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document.write( "Let centre of required circles be (a,0), radius given = 4<BR>\n" );
document.write( "Draw figure joining centres and applying pythagoras theorem, we get,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281-a%29%5E2+%2B+3%5E2+=+%28r%2BR%29%5E2 ALIGN=MIDDLE  ALT=\"%281-a%29%5E2+%2B+3%5E2+=+%28r%2BR%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2a%2B1%2B9=%281%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2-2a%2B1%2B9=%281%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2-2a-15+=+0 ALIGN=MIDDLE  ALT=\"a%5E2-2a-15+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=> a = 5 or a = -3\r<BR>\n" );
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document.write( "So, centre of required circles are (5,0) and (-3,0)<BR>\n" );
document.write( "And equations are:-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+%2B+y%5E2+=+4%5E2 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+%2B+y%5E2+=+4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E2+%2B+y%5E2+=+4%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E2+%2B+y%5E2+=+4%5E2\"   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%2By%5E2-10x%2B9=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2-10x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2%2B6x-7=0 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2%2B6x-7=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );