document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154836>Question 1154836</A>: <I><SPAN STYLE=\"word-break: break-all;\">  describe how the conic was formed using the<BR>\n" );
document.write( "concept of locus. its a parabola y^2+x+10y+26=0<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #777331 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=777331\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "A parabola is the locus of points equidistant from a fixed line (the directrix) and a fixed point (the focus).<br><BR>\n" );
document.write( "Put the equation in vertex form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2 ALIGN=MIDDLE  ALT=\"%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Bx%2B10y%2B26=0 ALIGN=MIDDLE  ALT=\"y%5E2%2Bx%2B10y%2B26=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-y%5E2-10y-26 ALIGN=MIDDLE  ALT=\"x+=+-y%5E2-10y-26\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%28y%5E2%2B10y%2B26%29 ALIGN=MIDDLE  ALT=\"x+=+-1%28y%5E2%2B10y%2B26%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+=+-1%28y%5E2%2B10y%2B25%29-1 ALIGN=MIDDLE  ALT=\"x+=+-1%28y%5E2%2B10y%2B25%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-1%28y%2B5%29%5E2-1 ALIGN=MIDDLE  ALT=\"x+=+-1%28y%2B5%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=%28x%2B1%29+=+-1%28y%2B5%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B1%29+=+-1%28y%2B5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation in this form tells us that the vertex is at (h,k) = (-1,-5).<br><BR>\n" );
document.write( "It also tells us that<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%284p%29+=+-1 ALIGN=MIDDLE  ALT=\"1%2F%284p%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+-1%2F4 ALIGN=MIDDLE  ALT=\"p+=+-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "p is the directed distance from the directrix to the vertex, so from the directrix to the vertex is -1/4.  Since the vertex is (-1,-5), the directrix is the line x = -3/4.<br><BR>\n" );
document.write( "p is also the directed distance from the vertex to the focus; since the vertex is (-1,-5), the focus is (-5/4,-5).<br><BR>\n" );
document.write( "So this parabola is the set of points equidistant from the line x=-3/4 and the point (-5/4,-5).<br><BR>\n" );
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