document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389891>Question 389891</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent line to the curve x^2 +2xy-y^2 +x=2 at (1,2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276413 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=276413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find the equation of the tangent line <BR>\n" );
document.write( "to the curve x^2 +2xy-y^2 +x=2 at (1,2)<BR>\n" );
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document.write( "Derivative:<BR>\n" );
document.write( "2x + 2[xy'+y]-2yy'+1= 0<BR>\n" );
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document.write( "Solve for y':<BR>\n" );
document.write( "2x + 2xy' +2y - 2yy' + 1 =0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y'(2x-2y) = -[2x+2y+1]<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y' = -[2x+2y+1]/[2x-2y]<BR>\n" );
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document.write( "Slope at (1,2) = -[2+4+1]/[2-4]<BR>\n" );
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document.write( "Slope at (1,2) = 7/2<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=================== <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );