document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=752632>Question 752632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of the circle circumscribing the triangle determined by the lines x+y=8, 2x+y=14 and 3x+y=22 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #457915 by </B><A HREF=/tutors/aboutme.mpl?userid=dkppathak><B>dkppathak(439)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dkppathak><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=dkppathak><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=457915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> triangle determined by lines are x+y=8, 2x+y=14 and 3x+y=22<BR>\n" );
document.write( "solving these equations in two groups by elimination <BR>\n" );
document.write( "x+y=8, 2x+y=14  we will get  x=6  and y=2 so vertex coordinates are (6 2)<BR>\n" );
document.write( "similarly  2x+y=14 and 3x+y=22  we will get vertex as (8 -2)<BR>\n" );
document.write( "           x+y=8,  3x+y=22 we will get vertex  as (7 1)<BR>\n" );
document.write( "therefore the circle will pass through vertex of triangle <BR>\n" );
document.write( "circle passing through  (6 2) (8 -2) and (7 1)<BR>\n" );
document.write( "we know that general  equation of circle<BR>\n" );
document.write( "x^2+y^2+2gx+2fy+c=0\r<BR>\n" );
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document.write( "circle passing through(6 2)  will be <BR>\n" );
document.write( "12g+4f+c= -40 (i)\r<BR>\n" );
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document.write( "circle passing through   (8 -2)  will be <BR>\n" );
document.write( "16g-4f+c=-68 (ii)<BR>\n" );
document.write( "circle passing through   (7 1) we will get <BR>\n" );
document.write( "14g +2f +c =-50 (iii)<BR>\n" );
document.write( "by solving equations in two groups<BR>\n" );
document.write( "12g+4f+c= -40 (i)<BR>\n" );
document.write( "16g-4f+c=-68<BR>\n" );
document.write( " we will get<BR>\n" );
document.write( "-4g+8f =28<BR>\n" );
document.write( "same way using two equation <BR>\n" );
document.write( "16g-4f+c=-68<BR>\n" );
document.write( "14g +2f +c =-50(iv)<BR>\n" );
document.write( " we will get <BR>\n" );
document.write( "2g-6f=-18  (v)<BR>\n" );
document.write( "by solving equation (iv) and (v)<BR>\n" );
document.write( "we will get <BR>\n" );
document.write( "f=2 and g=-3<BR>\n" );
document.write( "by putting value of g and f in equation (iii)<BR>\n" );
document.write( "we will get  c=-12<BR>\n" );
document.write( "arranging these value of g=-3   f=2  and c=-12 in general equations of circle<BR>\n" );
document.write( "equation of circle will be<BR>\n" );
document.write( "x^2 +y^2-6x+4y-12 =0<BR>\n" );
document.write( "ANSWER equation of circle subscribe the triangle will be<BR>\n" );
document.write( "x^2 +y^2-6x+4y-12 =0\r<BR>\n" );
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document.write( " </SPAN>\n" );
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