document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155426>Question 1155426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 78 inches, how deep is the mirror in the center? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778033 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=778033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Consider the origin of a coordinate system at the vertex of the parabola.  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.  Given that that distance is 32 feet, the equation for this parabolic mirror is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F128%29x%5E2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F128%29x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The distance across the top of the mirror is 78 inches, or 13/2 feet; halfway across is 13/4 feet.<br><BR>\n" );
document.write( "The depth of the mirror in the center is the y value at the edge of the top of the mirror:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F128%29%2813%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F128%29%2813%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.08252 feet to several decimal places, or 0.990 inches.<br><BR>\n" );
document.write( "ANSWER: the mirror is just under 1 inch deep at its center.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );