document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=652125>Question 652125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of the tangent line to the ellipse x^2/9 +y^2/4=1 at (3/2,3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #407901 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=407901\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  The equation of the tangent line to the ellipse <BR>\n" );
document.write( "x^2/9 +y^2/4=1 at (3/2,3)<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "Take the derivative:<BR>\n" );
document.write( "(2/9)x +(1/2)y*y' = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve for y':<BR>\n" );
document.write( "y' = [(-2x/9)/(y/2)]<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Evaluate at (3/2,3)<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "y' = -3 / (3/2)<BR>\n" );
document.write( "----<BR>\n" );
document.write( "y' -2<BR>\n" );
document.write( "==========<BR>\n" );
document.write( "Form: y = mx + b<BR>\n" );
document.write( "3 = -2(3/2) + b<BR>\n" );
document.write( "3 = -3 + b<BR>\n" );
document.write( "b = 5<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Equation of tangent line:<BR>\n" );
document.write( "y = -2x + 5<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );