document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=529653>Question 529653</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Identify conic section represented by the equation:<BR>\n" );
document.write( "4y^2 + 19 + 3x - 16y = 0<BR>\n" );
document.write( "Guess = Parabola since it only has one squared\r<BR>\n" );
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document.write( "Write the equation of the conic section in standard form:<BR>\n" );
document.write( "4y^2 + 19 + 3x - 16y = 0\r<BR>\n" );
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document.write( "I got (y-2)^2 = [-3(x+1)]/4. Is that in standard form?\r<BR>\n" );
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document.write( "Analytically determine equation of the line that is tangent to conic section at provided point:<BR>\n" );
document.write( "(-13, 5) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #349654 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=349654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify conic section represented by the equation:<BR>\n" );
document.write( "4y^2 + 19 + 3x - 16y = 0<BR>\n" );
document.write( "Guess = Parabola since it only has one squared<BR>\n" );
document.write( "It is a parabola.<BR>\n" );
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document.write( "Write the equation of the conic section in standard form:<BR>\n" );
document.write( "4y^2 + 19 + 3x - 16y = 0\r<BR>\n" );
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document.write( "I got (y-2)^2 = [-3(x+1)]/4. Is that in standard form?<BR>\n" );
document.write( "Standard form is x = a(y - k)^2 + h<BR>\n" );
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document.write( "Starting with (y-2)^2 = [-3(x+1)]/4<BR>\n" );
document.write( "4(y-2)^2 = [-3(x+1)]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1+=+%28-4%2F3%29%28y-2%29%5E2 ALIGN=MIDDLE  ALT=\"x%2B1+=+%28-4%2F3%29%28y-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4%2F3%29%2A%28y-2%29%5E2+-+1 ALIGN=MIDDLE  ALT=\"x+=+%28-4%2F3%29%2A%28y-2%29%5E2+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Analytically determine equation of the line that is tangent to conic section at provided point:<BR>\n" );
document.write( "(-13, 5)<BR>\n" );
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document.write( "I don't know what methods you're allowed or expected to use to do this.<BR>\n" );
document.write( "I'll differentiate implicitly:<BR>\n" );
document.write( "4y^2 + 19 + 3x - 16y = 0<BR>\n" );
document.write( "8y*dy + 3dx - 16dy = 0<BR>\n" );
document.write( "dy*(8y - 16) = -3dx<BR>\n" );
document.write( "y' = dy/dx = -3/(8y - 16)<BR>\n" );
document.write( "y'(5) = -1/8<BR>\n" );
document.write( "m @ (-13,5) = -1/8<BR>\n" );
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