document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=331802>Question 331802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of a circle touching the lines x-3y-11=0 and 3x-y-9=0 and having its center on the line x+2y+19=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #237827 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=237827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the equation of a circle touching the lines x-3y-11=0 and 3x-y-9=0 and having its center on the line x+2y+19=0.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Find the bisector of the two tangent lines, x-3y-11=0 and 3x-y-9=0.<BR>\n" );
document.write( "To do that, find the intersection of the 2 lines.<BR>\n" );
document.write( "The slope of the bisector is tan(arctan(1 line) + arctan(other line))<BR>\n" );
document.write( "The slope = 1<BR>\n" );
document.write( "With the slope and the point of intersection, find the equation of the bisector.<BR>\n" );
document.write( "Then find the intersection of the bisector and the line x+2y+19 = 0.  That's the center of the circle.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Find the distance from the center to either x-3y-11=0 or 3x-y-9=0, that's the radius.<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "email for any assistance needed at moralloophole@aol.com<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );