document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=380177>Question 380177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the tangent and normal to the conic 4x^2 + 9y^2 = 40 at point (1,-2). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #269955 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=269955\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the ellipse <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2+%2B+9y%5E2+=+40 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B+9y%5E2+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >, if we differentiate with respect to x, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+%2B+18y%28dy%2Fdx%29+=+0 ALIGN=MIDDLE  ALT=\"8x+%2B+18y%28dy%2Fdx%29+=+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=dy%2Fdx+=+-8+x%2F18+y+=+-4+x%2F9+y ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+-8+x%2F18+y+=+-4+x%2F9+y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore the slope at (1, -2) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4%2A1%29%2F%289%2A-2%29+=+2%2F9 ALIGN=MIDDLE  ALT=\"%28-4%2A1%29%2F%289%2A-2%29+=+2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Given slope 2/9 and a point (1, -2) we can easily find the y-intercept:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2+=+%282%2F9%29%281%29+%2B+b ALIGN=MIDDLE  ALT=\"-2+=+%282%2F9%29%281%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-20%2F9 ALIGN=MIDDLE  ALT=\"b+=+-20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus the equation of the line tangent to the ellipse at (1, -2) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%282%2F9%29x+-+20%2F9 ALIGN=MIDDLE  ALT=\"y+=+%282%2F9%29x+-+20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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