document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=114527>Question 114527</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the parabola described: Focus at (0,2); vertex at (0,0). Graph the parabola and the directrix.  Please explain.  Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #83771 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=83771\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first thing we know about this parabola is that the axis of symmetry is the line x = 0.  We know this because the both the focus and the vertex have to lie on the same line and the only line that passes through both (0,2) and (0,0) is x = 0, or the y-axis.\r<BR>\n" );
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document.write( "The next thing is to determine the distance between the focus and the vertex.  We can really just tell by inspection that the distance is 2 because both points are on a vertical line with the y coordinates differing by 2.  But, just to show the general case, lets use the distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29=sqrt%28%280-0%29%5E2%2B%282-0%29%5E2%29=sqrt%282%5E2%29=2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the equation for a parabola is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4p%28y-k%29=%28x-h%29%5E2 ALIGN=MIDDLE  ALT=\"4p%28y-k%29=%28x-h%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where p is the distance from the focus to the vertex, and the vertex is at point(h,k).  So,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%282%29%28y-0%29=%28x-0%29%5E2 ALIGN=MIDDLE  ALT=\"4%282%29%28y-0%29=%28x-0%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y=x%5E2 ALIGN=MIDDLE  ALT=\"8y=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2%29%2F8 ALIGN=MIDDLE  ALT=\"y=%28x%5E2%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The directrix is a line perpendicular to the axis of symmetry -p units distant from the vertex.  Since our parabola has a vertical line as an axis of symmetry, the directrix must be a horizontal line.  The only horizontal line that is -2 units from the vertex (0,0) is y = -2.\r<BR>\n" );
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document.write( "The green line is the directrix\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2%2F8%2C-2%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2Cx%5E2%2F8%2C-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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