document.write( "Question 32254: write the equation of a parabola with focus (0,4) and directrix y=-4 \n" ); document.write( "
Algebra.Com's Answer #18782 by AnlytcPhil(1806)\"\" \"About 
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write the equation of a parabola with focus (0,4) and directrix y=-4\r\n" );
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document.write( "Some books give the standard form of a y-parabola as\r\n" );
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document.write( "(1)                    y = a(x - h)² + k\r\n" );
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document.write( "and others give this as its standard form.\r\n" );
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document.write( "(2)             (x - h)² = 4p(y - k)\r\n" );
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document.write( "It doesn't matter which your book uses.  They are equivalent if a = 1/(4p)\r\n" );
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document.write( "The vertex of a parabola is the point halfway between the focus and the\r\n" );
document.write( "directrix.  The point halfway between the focus (0,4) and the horizontal\r\n" );
document.write( "directrix y=-4 is the origin (0,0), so if your book uses (1), then it is of\r\n" );
document.write( "the form \r\n" );
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document.write( "(3)                    y = ax² \r\n" );
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document.write( "If your book uses (2), then it is of the form:\r\n" );
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document.write( "(4)                   x² = 4py\r\n" );
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document.write( "p represents the distance from the vertex to the focus, which is considered a\r\n" );
document.write( "positive number if the directrix is below the vertex and focus, and negative\r\n" );
document.write( "number if the directrix is above the vertex and focus.\r\n" );
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document.write( "In this case p = +4, so a = 1/(4(4)) or 1/16\r\n" );
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document.write( "If your book uses form (1), then the answer is \r\n" );
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document.write( "(5)                    y = (1/16)x²    \r\n" );
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document.write( "If your book uses form (2), then the answer is x² = 4(4)y or\r\n" );
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document.write( "(6)                   x² = 16y\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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