document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1010264>Question 1010264</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent line to the curve (x-y)^2=2x+1  at the point (4,1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625709 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=625709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent line to the curve (x-y)^2=2x+1  at the point (4,1).<BR>\n" );
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document.write( "(x-y)^2=2x+1<BR>\n" );
document.write( "x^2 - 2xy + y^2 = 2x+1<BR>\n" );
document.write( "Differentiate implicitly<BR>\n" );
document.write( "2xdx - 2ydx - 2xdy + 2ydy = 2dx<BR>\n" );
document.write( "xdx - ydx - xdy + ydy - dx = 0<BR>\n" );
document.write( "(x-y-1)dx - (x - y)dy = 0<BR>\n" );
document.write( "(x-y-1)dx = (x - y)dy<BR>\n" );
document.write( "dy/dx = (x-y-1)/(x-y)<BR>\n" );
document.write( "@ (4,1) dy/dx = 2/3<BR>\n" );
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document.write( "y-1 = (2/3)(x-4)\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );