document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015843>Question 1015843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of a circle passing through (-1,6) and tangent to the lines x-2y+8=0 and 2x+y+6=0. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #632265 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=632265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The other tutor misread it, and used (-1,6) as the center of the circle.<BR>\n" );
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document.write( "Find the equation of a circle passing through (-1,6) and tangent to the lines x-2y+8=0 and 2x+y+6=0<BR>\n" );
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document.write( "Find the intersection of the 2 lines.<BR>\n" );
document.write( "x - 2y + 8 = 0<BR>\n" );
document.write( "2x + y + 6 = 0<BR>\n" );
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document.write( "x - 2y + 8 = 0<BR>\n" );
document.write( "4x +2y + 12 = 0 2nd eqn times 2<BR>\n" );
document.write( "----------------------------------- Add<BR>\n" );
document.write( "5x + 20 = 0<BR>\n" );
document.write( "x = -4<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "--> (-4,2)<BR>\n" );
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document.write( "The center of the circle will be on the bisector of the 2 lines, the point (h,k).<BR>\n" );
document.write( "The slopes of the lines are 22 and 1/2 --> they're perpendicular.<BR>\n" );
document.write( "The angle of x - 2y + 8 = 0 with the x-axis is arctan(1/2) =~ 26.565 degs<BR>\n" );
document.write( "Add 45 --> 71.565 degs<BR>\n" );
document.write( "m = tan(71.565) = 3<BR>\n" );
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document.write( "Find the eqn of the bisector: m = 3 thru (-4,2)<BR>\n" );
document.write( "--> y-2 = 3(x+4)<BR>\n" );
document.write( "The center of the circle is on this line, and is equidistant from the 2 given lines and the point (-1,6)<BR>\n" );
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document.write( "Using the line x - 2y + 8 = 0<BR>\n" );
document.write( "Distance to the line d = |h - 2k + 8|/sqrt(5)<BR>\n" );
document.write( "Distance to (-1,6) = sqrt((h+1)^2 + (k-6)^2)<BR>\n" );
document.write( "sqrt((h+1)^2 + (k-6)^2) = |h - 2k + 8|/sqrt(5)<BR>\n" );
document.write( "Square both sides<BR>\n" );
document.write( "(h+1)^2 + (k-6)^2 = |h - 2k + 8|^2/5<BR>\n" );
document.write( "h^2 + 2h + 1 + k^2 - 12k + 36 = (h^2 - 4hk + 6k^2 - 16h - 32k + 64)/5<BR>\n" );
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document.write( "That's a mess.<BR>\n" );
document.write( "I'll work on this later. </SPAN>\n" );
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