document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266674>Question 266674</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the equation of a tangent line to the curve x^2+y^2=169 at the point (5,-12) is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195914 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> step 1 -  we take a derivative of both sides and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+%2B+2y%28dy%2Fdx%29+=+0 ALIGN=MIDDLE  ALT=\"2x+%2B+2y%28dy%2Fdx%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 2 - solve for dy/dx<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29+=+-x%2Fy ALIGN=MIDDLE  ALT=\"%28dy%2Fdx%29+=+-x%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "step 3 - put your coordinates in and get<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28dy%2Fdx%29+=+-5%2F-12 ALIGN=MIDDLE  ALT=\"%28dy%2Fdx%29+=+-5%2F-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "so, the slope is<BR>\n" );
document.write( "dy/dx = m = 5/12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "step 4 - using slope and our coordinate as well as y = mx + b, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx+%2B+b ALIGN=MIDDLE  ALT=\"y+=+mx+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12+=+%285%2F12%29%2A5+%2B+b ALIGN=MIDDLE  ALT=\"-12+=+%285%2F12%29%2A5+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "solving for b, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-169%2F12+=+b ALIGN=MIDDLE  ALT=\"-169%2F12+=+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "step 5 - final equation is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%285%2F12%29x+-+169%2F12 ALIGN=MIDDLE  ALT=\"y+=+%285%2F12%29x+-+169%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );