document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=475425>Question 475425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of k for which the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+%2B+kx+=+8 ALIGN=MIDDLE  ALT=\"y+%2B+kx+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a tangent to the curve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E%282%29+%2B+4y+=+20 ALIGN=MIDDLE  ALT=\"%28x%29%5E%282%29+%2B+4y+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "*PLEASE ANSWER AS SOON AS POSSIBLE BRO :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326039 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=326039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We could use calculus or a graph (actually, the graph still helps as it gives a good visual), but the easiest way to do it is to treat them as functions of y and set them equal.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y = -\frac{1}{4}x^2 + 5 = 8 - kx\">\r<BR>\n" );
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document.write( "Since the quadratic is differentiable everywhere, we can say that a tangency point occurs when the equation has only one solution for x. We turn this into a quadratic in terms of x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{1}{4}x^2 - kx + 3 = 0\">, set the discriminant equal to zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE k^2 - 4(\frac{1}{4})(3) = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE k^2 - 3 = 0 \Rightarrow k = \pm \sqrt{3}\"> </SPAN>\n" );
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