document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019836>Question 1019836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle touching the line 4x-3y=28 at (4,-4) and passing through (-3,-5).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635768 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=635768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the circle touching the line 4x-3y=28 at (4,-4) and passing through (-3,-5).<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "The center of the circle is on the line perpendicular to the given line thru (4,-4).<BR>\n" );
document.write( "The slope of the line is -3/4 --> y+4 = (-3/4)*(x-4)<BR>\n" );
document.write( "--> y = -3x/4 - 1<BR>\n" );
document.write( "----<BR>\n" );
document.write( "The slope of a line tangent to a circle is -x/y.<BR>\n" );
document.write( "The center of the circle is also on the line perpendicular to the tangent line thru (-3,-5).<BR>\n" );
document.write( "The slope of the tangent line = -3/5.<BR>\n" );
document.write( "The slope of the line perpendicular = 5/3<BR>\n" );
document.write( "--> y+5 = (5/3)*(x+3)<BR>\n" );
document.write( "--> y = 5x/3<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The center of the circle is the intersection of y = 5x/3 and y = -3x/4 - 1<BR>\n" );
document.write( "5x/3 = -3x/4 - 1<BR>\n" );
document.write( "20x = -9x - 12<BR>\n" );
document.write( "x = -12/29 --> y = -20/29<BR>\n" );
document.write( "Center at (-12/29,-20/29)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "r = distance from the center to (4,-4)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+%28-4%2B20%2F29%29%5E2+%2B+%284%2B12%2F29%29%5E2+=+%2896%5E2+%2B+128%5E2%29%2F841 ALIGN=MIDDLE  ALT=\"r%5E2+=+%28-4%2B20%2F29%29%5E2+%2B+%284%2B12%2F29%29%5E2+=+%2896%5E2+%2B+128%5E2%29%2F841\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+12%2F29%29%5E2+%2B+%28y+%2B+20%2F29%29%5E2+=+%28160%2F29%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+%2B+12%2F29%29%5E2+%2B+%28y+%2B+20%2F29%29%5E2+=+%28160%2F29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "====================================================<BR>\n" );
document.write( "Something is wrong, I'll check it later.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "I can't find the error.  If you can't find it, repost it, maybe someone else will do it.<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "I see what the problem is.  A slope of -x/y for a circle applies to circles centered at the Origin.<BR>\n" );
document.write( "I'll work on this later today. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );