document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180349>Question 1180349</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A flashlight is shaped like a paraboloid, so that if its light bulb is placed at the focus, the light rays from the bulb will then bounce of the surface in a<BR>\n" );
document.write( "focused direction that is parallel to the axis. If the paraboloid has a depth of<BR>\n" );
document.write( "1.8 in and the diameter on its surface is 6 in, how far should the light source<BR>\n" );
document.write( "be placed from the vertex?​ </SPAN>\n" );
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document.write( "Consider a cross section of the paraboloid as a parabola with vertex at the origin.  Then the equation of the parabola is<br><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><BR>\n" );
document.write( "where p is the distance from the vertex to the focus.<br><BR>\n" );
document.write( "With a depth of 1.8 inches and a diameter of 6 inches, a point on the parabola is (3,1.8).  Use that point in the equation of the parabola to determine p.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.8+=+%281%2F%284p%29%29%283%5E2%29 ALIGN=MIDDLE  ALT=\"1.8+=+%281%2F%284p%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%2F9+=+1%2F5+=+1%2F%284p%29 ALIGN=MIDDLE  ALT=\"1.8%2F9+=+1%2F5+=+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=4p=5 ALIGN=MIDDLE  ALT=\"4p=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=5%2F4=1.25 ALIGN=MIDDLE  ALT=\"p=5%2F4=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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