document.write( "Question 1150068: 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 60 feet across at its opening and 5 feet deep at its center, where should the receiver be placed?\r
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Algebra.Com's Answer #771429 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "First, we need to derive the equation of the parabola.\r\n" );
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document.write( "Standard form equation of a parabola is y = .\r\n" );
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document.write( "Since the parabola is 60 feet wide at 5 feet from its vertex, it means that y = 5 at x = 30\r\n" );
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document.write( "    5 = ,  which implies  a =  = .\r\n" );
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document.write( "Thus the standard equation of the parabola is  \r\n" );
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document.write( "             y =      (1)\r\n" );
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document.write( "under given conditions.\r\n" );
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document.write( "Next, it is well known fact that if the parabola has the form  y = ,  then the focus of the parabola is at y = \r\n" );
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document.write( "    (see the lesson  Parabola definition, canonical equation, characteristic points and elements  at this site).\r\n" );
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document.write( "Comparing it with the equation, we get  2p = 180,  i.e.  p =  = 90.\r\n" );
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document.write( "Hence, receiver should be placed on the parabola axis at the distance of   =  = 45 feet from the vertex.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On parabolas, see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Parabola definition, canonical equation, characteristic points and elements \r
\n" ); document.write( "\n" ); document.write( "    - Parabola focal property \r
\n" ); document.write( "\n" ); document.write( "    - Tangent lines and normal vectors to a parabola \r
\n" ); document.write( "\n" ); document.write( "    - Optical property of a parabola\r
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\n" ); document.write( "\n" ); document.write( "    - Practical problems from the archive related to ellipses and parabolas \r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on parabolas. \r
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