document.write( "Question 1091793: Parabola\r
\n" ); document.write( "\n" ); document.write( "The antenna of a radio telescope is paraboloid measuring 81 feet across with depth of 16 feet. Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.\r
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Algebra.Com's Answer #706523 by ikleyn(52803)\"\" \"About 
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\n" ); document.write( "The antenna of a radio telescope is paraboloid measuring 81 feet across with depth of 16 feet.
\n" ); document.write( "Determine, to the nearest tenth of a foot, the distance from the vertex to the focus of this antenna.
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document.write( "If you read the lesson\r\n" );
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document.write( "    - Parabola definition, canonical equation, characteristic points and elements \r\n" );
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document.write( "in this site, you will learn that if you write the canonical equation of a parabola in the form\r\n" );
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document.write( "y = \"%281%2F%282%2Ap%29%29%2Ax%5E2\",     (1)\r\n" );
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document.write( "then the distance from the parabola's vertex (0,0) to the parabola's focus  (focal distance) is  \"p%2F2\".\r\n" );
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document.write( "So, our nearest task is to present the equation of our parabola in the form (1).\r\n" );
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document.write( "For it, substitute y = 16 (depth in feet)  and  x = \"81%2F2\"  into equation (1). You will get then\r\n" );
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document.write( "16 = \"%281%2F%282%2Ap%29%29%2A%2881%2F2%29%5E2\",   or  2p = \"%28%2881%2F2%29%5E2%29%2F16\" = \"81%5E2%2F%284%2A16%29\".\r\n" );
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document.write( "Then  p = \"81%5E2%2F%288%2A16%29\" = 51.258.\r\n" );
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document.write( "Thus the focal distance is  \"p%2F2\" = \"51.258%2F2\" = 25.629 ft.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The focal distance is 25.629 ft.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic
\n" ); document.write( "\"Conic sections: Parabolas. Definition, major elements and properties. Solved problems\".\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II\r
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