document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1014205>Question 1014205</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The circle is tangent to the line 3x -4y =34 at point (10,-1) and also tangent to the line 4x+3y=12 at point (3,0). Find the equation of the circle in general form </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #630556 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=630556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) A tangent to a circle is perpendicular to the radius at the point of tangency<BR>\n" );
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document.write( "2) The slope of the radius is the negative reciprocal of the tangent line's slope<BR>\n" );
document.write( "We have two lines<BR>\n" );
document.write( "3x -4y = 34 and 4x +3y = 12, solve each one for y<BR>\n" );
document.write( "y = 3x/4 -17/2 and y = -4x/3 + 4<BR>\n" );
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document.write( "3) now we can write two equations for the radius line<BR>\n" );
document.write( "y = -4/3 x + b<BR>\n" );
document.write( "y = 3x/4 + b<BR>\n" );
document.write( "now use the point of tangency for each line to determine the b<BR>\n" );
document.write( "-1 = -4(10)/3 + b<BR>\n" );
document.write( "-3 = -40 + 3b<BR>\n" );
document.write( "3b = 37<BR>\n" );
document.write( "b = 37/3<BR>\n" );
document.write( "y = -4x/3 + 37/3<BR>\n" );
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document.write( "0 = 3*3/4 + b<BR>\n" );
document.write( "b = -9/4<BR>\n" );
document.write( "y = 3x/4 + 9/4<BR>\n" );
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document.write( "4) set the two lines = to each other and solve for x<BR>\n" );
document.write( "-4x/3 + 37/3 = 3x/4 + 9/4<BR>\n" );
document.write( "-16x + 148 = 9x + 27<BR>\n" );
document.write( "25x = 121<BR>\n" );
document.write( "x = 121 / 25 = 4.84<BR>\n" );
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document.write( "5) substitute for x in either equation for r to get the y coordinate<BR>\n" );
document.write( "pick y = 3x/4 + 9/4<BR>\n" );
document.write( "y = 3(4.84) / 4 + 9/4<BR>\n" );
document.write( "y = 0.75*4.84 + 2.25<BR>\n" );
document.write( "y = 5.88<BR>\n" );
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document.write( "6) center of circle is (4.84, 5.88)<BR>\n" );
document.write( "to find r use distance formula from center to point of tangency, pick (3, 0)<BR>\n" );
document.write( "distance(d) = sqrt((4.84-3)^2 + 5.88^2)<BR>\n" );
document.write( "d = 6.16116872 approx 6.16<BR>\n" );
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document.write( "7)general form of circle is<BR>\n" );
document.write( "(x-4.84)^2 + (y-5.88)^2 = 6.16^2<BR>\n" );
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