document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=917415>Question 917415</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #556654 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=556654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the focus is at (0,5)<BR>\n" );
document.write( "the directrix is at y = -5<BR>\n" );
document.write( "the vertex is halftway between the focus and the intersection of the directrix with the axis of symmetry.<BR>\n" );
document.write( "that would make the vertex at (0,0).\r<BR>\n" );
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document.write( "the vertex form of the equation of a parabola is:\r<BR>\n" );
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document.write( "y = a * (x-h)^2 + k\r<BR>\n" );
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document.write( "the conic form of the equation of a parabola is:\r<BR>\n" );
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document.write( "4p * (y-k) = (x-h)^2\r<BR>\n" );
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document.write( "p is the distance from the directrix to the vertex and from the vertex to the focus.\r<BR>\n" );
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document.write( "that makes p half the distance between the focus and the directrix on the axis of symmetry.\r<BR>\n" );
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document.write( "that makes p = 5.\r<BR>\n" );
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document.write( "from the conic form of the equation of a parabola, you get:\r<BR>\n" );
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document.write( "4p * (y-k) = (x-h)^2\r<BR>\n" );
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document.write( "since the vertex is at (0,0), this equation becomes:\r<BR>\n" );
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document.write( "4p * y = x^2\r<BR>\n" );
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document.write( "since p = 5, this equation becomes:\r<BR>\n" );
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document.write( "20 * y = x^2\r<BR>\n" );
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document.write( "divide both sides of this equation by 20 and you get:\r<BR>\n" );
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document.write( "y = (1/20) * x^2\r<BR>\n" );
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document.write( "that's your equation.\r<BR>\n" );
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document.write( "in the vertex form of your equation, you have:\r<BR>\n" );
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document.write( "y = a(x-h)^2 + k\r<BR>\n" );
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document.write( "since h = 0 and k = 0 and a = 1/(4p) and p = 5, you then get:\r<BR>\n" );
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document.write( "y = (1/20) * x^2.\r<BR>\n" );
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document.write( "the vertex form of the equation and the conic form of the equation can be directly translated into each other with a = 1/(4p) or 4p = 1/a.\r<BR>\n" );
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document.write( "the graph of your equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/102702.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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