document.write( "Question 1204075: 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 48 feet across at its opening and 6 feet deep at its center, where should the receiver be placed? \n" ); document.write( "

Algebra.Com's Answer #840100 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Working the problem in 2 dimensions, we have an upward-opening parabola with vertex (0,0), with two other points at (-24,6) and (24,6).

\n" ); document.write( "The problem asks for where the receiver should be placed, which is at the focus of the parabola. Using the standard notation with p as the distance from the vertex to the focus, the equation of the parabola is

\n" ); document.write( " $\"y=%281%2F%284p%29%29x%5E2\"$

\n" ); document.write( "Determine p using (x,y)=(24,6).

\n" ); document.write( " $\"6=%281%2F%284p%29%29%2824%5E2%29\"$
\n" ); document.write( " $\"1%2F%284p%29=6%2F%2824%5E2%29=1%2F96\"$
\n" ); document.write( " $\"4p=96\"$
\n" ); document.write( " $\"p=24\"$

\n" ); document.write( "p, the distance from the vertex to the focus, is 24 feet, so the focus is at (0,24).

\n" ); document.write( "ANSWER: 24 feet above the vertex

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