document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164605>Question 1164605</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A flashlight shaped like paraboloid, so that if the bulb is focused, the light rays from the bulb is faced at the focus, the light rays from the bulb will then bounce off the surface in a focused direction that is parallel to the axis. If the paraboloid has a depth of 1.8 and the diameter is 6 in, how far should the light source be placed from the vertex?<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 #854201 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13327)</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=854201\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The response from the other tutor is fine.  In that response, she uses y = ax^2 for the equation of the parabola with the given dimensions to find that a = 0.2; then she uses the formula f = 1/(4a) to find that the distance from the vertex to the focus is 1.25 inches.<br><BR>\n" );
document.write( "I and many students are familiar with a slightly different convention which of course leads to the same result.<br><BR>\n" );
document.write( "The basic standard formula for the equation of a parabola that I am familiar with is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F%284a%29%29x%5E2 ALIGN=MIDDLE  ALT=\"y=%281%2F%284a%29%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where a is the distance from the vertex to the focus.  Using that to find the distance from the vertex to the focus directly...<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.8=%281%2F%284a%29%29%283%5E2%29 ALIGN=MIDDLE  ALT=\"1.8=%281%2F%284a%29%29%283%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.8=9%2F4a ALIGN=MIDDLE  ALT=\"1.8=9%2F4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.2a=9 ALIGN=MIDDLE  ALT=\"7.2a=9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=9%2F7.2=1.25 ALIGN=MIDDLE  ALT=\"a=9%2F7.2=1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 1.25 inches<br><BR>\n" );
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