document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798328>Question 798328</A>: <I><SPAN STYLE=\"word-break: break-all;\"> show that the line y=2x+3 is the equation of the tangent of the ellipse 4x^2+2y^2=2. hence find the coordinate of the point of contact </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482153 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39628)</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=482153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You would expect exactly one intersection point.  Substitute for y and solve for x.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B2%282x%2B3%29%5E2=2 ALIGN=MIDDLE  ALT=\"4x%5E2%2B2%282x%2B3%29%5E2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that substitution done,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B%282x%2B3%29%5E2=1 ALIGN=MIDDLE  ALT=\"2x%5E2%2B%282x%2B3%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B4x%5E2%2B12x%2B9=1 ALIGN=MIDDLE  ALT=\"2x%5E2%2B4x%5E2%2B12x%2B9=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2%2B12x%2B8=0 ALIGN=MIDDLE  ALT=\"6x%5E2%2B12x%2B8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x%2B4=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x%2B4=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=x=%28-6%2B-sqrt%2836-4%2A3%2A4%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28-6%2B-sqrt%2836-4%2A3%2A4%29%29%2F%282%2A3%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=%28-6%2B-sqrt%2836-48%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28-6%2B-sqrt%2836-48%29%29%2F%282%2A3%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=%28-6%2B-sqrt%28-12%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"x=%28-6%2B-sqrt%28-12%29%29%2F%282%2A3%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=%28-3%2B-+i%2Asqrt%283%29%29%2F%283%29 ALIGN=MIDDLE  ALT=\"x=%28-3%2B-+i%2Asqrt%283%29%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, apparently NOT tangent!  A COMPLEX solution!\r<BR>\n" );
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document.write( "I've checked this over twice.  You would not be expecting a complex solution, but you want instead a single real solution.  One of your equations must be wrong.  \r<BR>\n" );
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document.write( "A better look at the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-6%2C6%2C-6%2C6%2C-sqrt%28-2x%5E2%2B1%29%2Csqrt%28-2x%5E2%2B1%29%2C2x%2B3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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