Algebra.Com's Answer #849382 by ikleyn(52813)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "A flashlight is shaped like a paraboloid, so that if its light bulb is placed at the focus,
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document.write( "the light rays from the bulb will then bounce off the surface in a focused direction
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document.write( "that is parallel to the axis. if the paraboloid has a depth of 1.8 in and the diameter
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document.write( "on its surface is 6 in, how far should the light source be placed from the vertex?
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document.write( "If you are not familiar with the general theory and optical properties of parabolas, you may start reading 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( "We are given that the diameter of the paraboloid of revolution is 6 inches and its depth is 1.8 inch.\r\n" );
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document.write( "It means that if we consider the parabola as the section of the given paraboloid, it has an equation \r\n" );
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document.write( " y =  (1)\r\n" );
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document.write( "Indeed, this equation gives y = 1.8 at x = 3. \r\n" );
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document.write( "For such applications, the standard/canonical form of the parabola equation is\r\n" );
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document.write( " y =  , (2)\r\n" );
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document.write( "Then the general theory says that the distance from the parabola vertex to its focus, or focal distance,\r\n" );
document.write( "is  .\r\n" );
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document.write( "So, in our case, the parameter \"p\" in the equation (1) is equal to 5/2 = 2.5.\r\n" );
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document.write( " OK. Surely, we will place the light bulb in the focus of the parabola to use its optical property,\r\n" );
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document.write( " and we need to determine the distance from the focus to the parabola vertex.\r\n" );
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document.write( "According to the general theory, summarized above, the focus is located at the distance from the vertex.\r\n" );
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document.write( "So, the distance under the question is =  = 1.25 inches.\r\n" );
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document.write( "ANSWER. The light bulb should be placed at the distance of 1.25 inches from the paraboloid vertex.\r\n" );
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document.write( "Solved.\r
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