document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082777>Question 1082777</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent and normal to x^2 + 3xy + y^2 = 5 at P(1,1). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696869 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=696869\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent and normal to x^2 + 3xy + y^2 = 5 at P(1,1).<BR>\n" );
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document.write( "Find the 1st derivative<BR>\n" );
document.write( "x^2 + 3xy + y^2 = 5<BR>\n" );
document.write( "Differentiate implicitly.<BR>\n" );
document.write( "2xdx + 3ydx + 3xdy + 2ydy = 0<BR>\n" );
document.write( "(2x+3)dx + (2y+3)dy = 0<BR>\n" );
document.write( "dy/dx = -(2x+3)/(2y+3) = m, the slope<BR>\n" );
document.write( "At (1,1) m = -1<BR>\n" );
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document.write( "At (1,1), y-1 = -(x-1)<BR>\n" );
document.write( "y = -x + 2 is tangent.<BR>\n" );
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document.write( "y = x is normal\r<BR>\n" );
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