document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012198>Question 1012198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A searchlight has a parabolic reflector that forms a “bowl” which is 12 inches wide from rim to rim and 8 inches deep. If the filament of the light bulb is located at the focus, how far from the vertex of the reflector is it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628092 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=628092\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=x%5E2 ALIGN=MIDDLE  ALT=\"4py=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be a parabola with vertex at the origin, and opening upward.  Using different symbols, the parabola can also be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2 ALIGN=MIDDLE  ALT=\"y=ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and has points (-6,8) and (6,8).\r<BR>\n" );
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document.write( "Find the factor, a.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8=a%2A6%5E2 ALIGN=MIDDLE  ALT=\"8=a%2A6%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using the simpler formula.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8%2F36 ALIGN=MIDDLE  ALT=\"a=8%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2%2F9 ALIGN=MIDDLE  ALT=\"a=2%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The equation for the parabola more specifically can be  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%282%2F9%29x%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%282%2F9%29x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "What about the focus?<BR>\n" );
document.write( "Put the equation with the p into the same form as the more specific-found equation.  The value of p is THE DISTANCE FROM VERTEX TO FOCUS.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4py=x%5E2 ALIGN=MIDDLE  ALT=\"4py=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=%281%2F%284p%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=%281%2F%284p%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing the corresponding equation parts, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F9=1%2F%284p%29 ALIGN=MIDDLE  ALT=\"2%2F9=1%2F%284p%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F2=4p ALIGN=MIDDLE  ALT=\"9%2F2=4p\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=9%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"p=9%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=9%2F8%29 ALIGN=MIDDLE  ALT=\"highlight%28p=9%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The focus will be on the \"opening upward\" side of the parabola, as described in this discussion, above the origin, so the focus is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289%2F8=1%261%2F8%29 ALIGN=MIDDLE  ALT=\"highlight%289%2F8=1%261%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches away from the vertex.  Inside of the curve. </SPAN>\n" );
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