document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935929>Question 935929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this question. <BR>\n" );
document.write( "A tangent to the parabola x^2 = 16y is perpendicular to the line x - 2y - 3 = 0 .find the equation of this tangent and the coordinate of the point of conduct  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569298 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=569298\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2y=-x%2B3 ALIGN=MIDDLE  ALT=\"-2y=-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2F2-3%2F2 ALIGN=MIDDLE  ALT=\"y=x%2F2-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You want a slope of the desired line to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, negative reciprocal of that slope.  You do not know the y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x%2Bk ALIGN=MIDDLE  ALT=\"y=-2x%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  You want THIS line to intersect the parabola AT ONE POINT, ....\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16%28-2x%2Bk%29 ALIGN=MIDDLE  ALT=\"x%5E2=16%28-2x%2Bk%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-32x%2B16k ALIGN=MIDDLE  ALT=\"x%5E2=-32x%2B16k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B32x-16k=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B32x-16k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you need discriminant of this to be 0.  This will ensure the intersection will be ONE POINT.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-32%29%5E2-4%2A%28-16k%29=0 ALIGN=MIDDLE  ALT=\"%28-32%29%5E2-4%2A%28-16k%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024%2B64k=0 ALIGN=MIDDLE  ALT=\"1024%2B64k=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64k=-1024 ALIGN=MIDDLE  ALT=\"64k=-1024\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-16%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2x-16 ALIGN=MIDDLE  ALT=\"y=-2x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you want to know the intersection of this with the parabola <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16y ALIGN=MIDDLE  ALT=\"x%5E2=16y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=16%28-2x-16%29 ALIGN=MIDDLE  ALT=\"x%5E2=16%28-2x-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=-32x-256 ALIGN=MIDDLE  ALT=\"x%5E2=-32x-256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B32x%2B256=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B32x%2B256=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B16%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28x%2B16%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "THIS means, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-16%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the corresponding coordinate y is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-2%2A%28-16%29-16 ALIGN=MIDDLE  ALT=\"y=-2%2A%28-16%29-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=32-16 ALIGN=MIDDLE  ALT=\"y=32-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=16%29 ALIGN=MIDDLE  ALT=\"highlight%28y=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "NEXT:<BR>\n" );
document.write( "What is the line with slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and with the point (-16,16) ?<BR>\n" );
document.write( "Use the point-slope form equation for a line to form the equation of this line. </SPAN>\n" );
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