document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198607>Question 198607</A>: <I><SPAN STYLE=\"word-break: break-all;\">  write an equation of a parabola with a vertex (3,0) and a directix at x = 3.  I get that this information gives you a = 0 and this does not make sense.     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149127 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "It actually does make a perverse kind of sense.  What you have is a degenerate parabola, actually a straight line that isn't a parabola at all.  Here's why.\r<BR>\n" );
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document.write( "Since the given directrix is a vertical line, the axis of symmetry of this parabola is horizontal.  The vertex form of the equation of a parabola with vertex at (<i>h</i>,<i>k</i>) and directrix <i>x</i> = <i>h</i> - <i>p</i> is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (y - k)^2 = 4p(x - h)\">\r<BR>\n" );
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document.write( "So using the equation of the directrix to calculate <i>p</i> when (<i>h</i>,<i>k</i>) = (3, 0) and <i>x</i> = 3:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x = h - p = 3 - p = 3 \ \ \Rightarrow\ \ p = 0\">\r<BR>\n" );
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document.write( "So the equation becomes:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (y - 0)^2 = 4(0)(x - 3) = 0 \ \ \Rightarrow\ \ y = 0\">\r<BR>\n" );
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document.write( "Which is the equation of the <i>x</i>-axis.\r<BR>\n" );
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document.write( "Geometrically speaking, a parabola is formed by the intersection of a plane and a cone where the plane is parallel to one of the generators of the cone.  But if you move the plane to a point where the generator of the cone actually lies <i>wholly in</i> the plane, the parabola degenerates to a straight line.  The distance from the focus to the vertex (and the distance from the directrix to the vertex) is a function of the distance from the axis of symmetry that lies in the plane and the generator of the cone.  When that distance is zero, you have no parabola.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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