document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022660>Question 1022660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use implicit differentiation to find an equation of the tangent line to the ellipse at the given point.<BR>\n" );
document.write( "x^2/4 + y^2/10= 14, (4, 10)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638312 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F4+%2B+y%5E2%2F10=+14 ALIGN=MIDDLE  ALT=\"x%5E2%2F4+%2B+y%5E2%2F10=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then after differentiating implicitly and simplifying, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F2%2B%28y%28dy%2Fdx%29%29%2F5+=+0 ALIGN=MIDDLE  ALT=\"x%2F2%2B%28y%28dy%2Fdx%29%29%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting the coordinates of (4,10) into the last equation, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F2%2B%2810%28dy%2Fdx%29%29%2F5+=+0 ALIGN=MIDDLE  ALT=\"4%2F2%2B%2810%28dy%2Fdx%29%29%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B+2%28dy%2Fdx%29+=+0 ALIGN=MIDDLE  ALT=\"2%2B+2%28dy%2Fdx%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+-1 ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence the equation of the tangent line to the ellipse at the point (4,10) is \r<BR>\n" );
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document.write( "y-10 = -(x-4), or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+%2B+y+=+14%29 ALIGN=MIDDLE  ALT=\"highlight%28x+%2B+y+=+14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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