document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625669>Question 625669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the tangent line to the graph at the given point. 7x^2-6(sq3)xy+13y^2-16=0. (sq3,1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #393726 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393726\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Differentiate the equation implicitly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left(7x^2\ -\ 6\sqrt{3}xy\ +\ 13y^2\ -\ 16\right)\ =\ \frac{d0}{dx}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{d\left(7x^2\right)}{dx}\ -\ \frac{d\left(6\sqrt{3}xy\right)}{dx}\ +\ \frac{d\left(13y^2\right)}{dx}\ -\ \frac{d(16)}{dx}\ =\ 0\">\r<BR>\n" );
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document.write( "Use the Chain Rule and the Product Rule:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 14x\ -\ 6\sqrt{3}\left(x\frac{dy}{dx}\ +\ y\frac{dx}{dx}\right)\ +\ 13y\frac{dy}{dx}\ -\ 0\ =\ 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 14x\ -\ 6\sqrt{3}x\frac{dy}{dx}\ -\ 6\sqrt{3}y\ +\ 13y\frac{dy}{dx}\ =\ 0\">\r<BR>\n" );
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document.write( "Now take out a common factor of 2 and then solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dy}{dx}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{3\sqrt{3}y\ -\ 7x}{13y\ -\ 3\sqrt{3}x}\">\r<BR>\n" );
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document.write( "Do not succumb to the temptation to rationalize your denominator at this point.  We have an expression for the tangent to your ellipse at any point,  all that is needed now is to evaluate this expression at the given point.  Substitute the coordinates of the given point for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> in the expression for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dy}{dx}\"> and do the arithmetic.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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