document.write( "Question 30029: A searchlight reflector is designed so that a crass section through its axis is a parabola and the light source is at the focus. Find the focus if the reflector is 3 feet across the opening and 1 foot deep.\r
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Algebra.Com's Answer #16793 by AnlytcPhil(1807) $\"\"$ $\"About$

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A searchlight reflector is designed so that a crass section through its axis is\r\n" );
document.write( "a parabola and the light source is at the focus. Find the focus if the\r\n" );
document.write( "reflector is 3 feet across the opening and 1 foot deep. \r\n" );
document.write( "Where do I even start?!? I'm so lost!\r\n" );
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document.write( "The equation of a parabola whose vertex is at the origin (0,0) is\r\n" );
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document.write( "x² = 4py\r\n" );
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document.write( "where p is the distance from the vertex (0,0) to the focus.\r\n" );
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document.write( "The parabola must go through the points (±3/2,1) in order to be 3 feet across\r\n" );
document.write( "and 1 foot deep.  Substituting ±3/2 for x and 1 for y:\r\n" );
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document.write( "(±3/2)² = 4p(1)\r\n" );
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document.write( "9/4 = 4p\r\n" );
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document.write( "Solve for p by dividing both sides by 4, and 9/4 divided by 4 = 9/16, so\r\n" );
document.write( "p = 9/16 feet, or converting to inches 6 3/4 inches from the  \r\n" );
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document.write( "So the focus is 6 3/4 inches above the vertex and 5 1/4 inches below glass.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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