document.write( "Question 1091792: Parabola\r
\n" ); document.write( "\n" ); document.write( "A satellite dish has a shape of paraboloid. The signals that it receives is reflected to the receiver that is located at the focus of the paraboloid. If dish is 8 feet across at its opening and 1 foot deep at its vertex, determine the location (distance from the vertex of the dish) of its focus.\r
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Algebra.Com's Answer #706388 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A satellite dish has a shape of paraboloid. The signals that it receives is reflected to the receiver that is located
\n" ); document.write( "at the focus of the paraboloid. If dish is 8 feet across at its opening and 1 foot deep at its vertex, determine the location
\n" ); document.write( "(distance from the vertex of the dish) of its focus.
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document.write( "Let us represent the parabola by the equation y = \"ax%5E2\"  (1).\r\n" );
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document.write( "Then this phrase \" . . . dish is 8 feet across at its opening and 1 foot deep at its vertex\" means that\r\n" );
document.write( "the point (x,y) = (4,1) lies on the parabola.\r\n" );
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document.write( "In turn, it then  means that  y = 1 at  x = 4.\r\n" );
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document.write( "It implies that in the equation (1)   1 = \"a%2A4%5E2\",  or  a = \"1%2F16\".\r\n" );
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document.write( "So, the equation of the parabola is y = \"%281%2F16%29%2Ax%5E2\".\r\n" );
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document.write( "It is the canonical equation of the parabola\r\n" );
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document.write( "    (see the lesson Parabola definition, canonical equation, characteristic points and elements  in this site).\r\n" );
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document.write( "The vertex of this parabola is the point  (0,0)  (the origin of the coordinate system).\r\n" );
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document.write( "The focus of this parabola is the point  ( 0, \"%281%2F2%29%2A%2816%2F2%29\" ) = (0,4).\r\n" );
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document.write( "    (See again the lesson referred above).\r\n" );
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document.write( "Thus the distance from the vertex to the focus is 4 feet.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The distance from the vertex to the focus of the parabola / paraboloid is 4 feet.\r
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\n" ); document.write( "\n" ); document.write( "The solution by @josgarithmetic and his answer \"1 feet\" is \"highlight%28WRONG%29\".\r
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\n" ); document.write( "You have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    ALGEBRA-II - YOUR ONLINE TEXTBOOK.\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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