document.write( "Question 1165727: a satellite dish has a shaped of a paraboloid. If the receiver of the satellite dish is placed at the focus 2.53 ft from the vertex, write an equation for the cross-section of the satellite dish. Assume that the focus is on the positive x-axis and its vertex at the origin. \n" ); document.write( "

Algebra.Com's Answer #851400 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "a satellite dish has a $\"highlight%28cross%28shaped%29%29\"$ shape of a paraboloid. If the receiver of the satellite dish
\n" ); document.write( "is placed at the focus 2.53 ft from the vertex, write an equation for the cross-section
\n" ); document.write( "of the satellite dish. Assume that the focus is on the positive x-axis and its vertex at the origin.
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\n" ); document.write( "\n" ); document.write( "        It is a standard problem of this kind. The feature is\r
\n" ); document.write( "\n" ); document.write( "        that in this problem the symmetry line is parallel to x-axis,\r
\n" ); document.write( "\n" ); document.write( "        while usually in such problems the symmetry line is parallel to y-axis.\r
\n" ); document.write( "\n" ); document.write( "        So, I will adapt a standard solution to this case.\r
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document.write( "For solving such problems, write an equation of the parabola in the cross-section\r\n" );
document.write( "in the form\r\n" );
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document.write( "    x = .    (1)\r\n" );
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document.write( "The advantage of writing in this form is the fact that then \"p\"\r\n" );
document.write( "is the distance from the parabola vertex to its focus.\r\n" );
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document.write( "In this problem, the value of p is given: it is 2.53 ft.\r\n" );
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document.write( "So, we substitute this value into equation (1), and we get\r\n" );
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document.write( "    x = .\r\n" );
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document.write( "It gives the equation of the parabolic section \r\n" );
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document.write( "    x = ,  or  x = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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