document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198216>Question 1198216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 72 feet across at its opening and 6 feet deep at its center, where should the receiver be placed? (Hint: Draw a cross section of the dish on a graph and place the vertex at (0, -6) so that the opening of the dish lies on the x-axis).\r<BR>\n" );
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document.write( "Find the equation of the parabola.<BR>\n" );
document.write( "How far above the vertex should the receiver be placed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848335 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><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=848335\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Equation of the Parabola**\r<BR>\n" );
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document.write( "* **Vertex:** (0, -6) <BR>\n" );
document.write( "* **Point on the Parabola:** (36, 0) (Since the dish is 72 feet across, the point on the parabola is half of that, or 36 feet, from the vertex)\r<BR>\n" );
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document.write( "* **Standard Form of a Parabola:** <BR>\n" );
document.write( "   (x - h)² = 4p(y - k) <BR>\n" );
document.write( "   where (h, k) is the vertex\r<BR>\n" );
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document.write( "* **Substitute values:** <BR>\n" );
document.write( "   (x - 0)² = 4p(y - (-6)) <BR>\n" );
document.write( "   x² = 4p(y + 6)\r<BR>\n" );
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document.write( "* **Find the value of 'p':**<BR>\n" );
document.write( "   Substitute the point (36, 0) into the equation:<BR>\n" );
document.write( "   36² = 4p(0 + 6)<BR>\n" );
document.write( "   1296 = 24p<BR>\n" );
document.write( "   p = 1296 / 24<BR>\n" );
document.write( "   p = 54\r<BR>\n" );
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document.write( "* **Equation of the Parabola:** <BR>\n" );
document.write( "   x² = 4 * 54 * (y + 6)<BR>\n" );
document.write( "   x² = 216(y + 6)\r<BR>\n" );
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document.write( "**2. Find the Distance of the Receiver from the Vertex**\r<BR>\n" );
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document.write( "* The receiver should be placed at the focus of the parabola.<BR>\n" );
document.write( "* The distance from the vertex to the focus is 'p'.\r<BR>\n" );
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document.write( "* **Receiver Distance:** 54 feet\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* The equation of the parabola is: x² = 216(y + 6)<BR>\n" );
document.write( "* The receiver should be placed 54 feet above the vertex of the dish.<BR>\n" );
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