Algebra.Com's Answer #663548 by Edwin McCravy(20055)![\"\"](\"/images/stars/stars-13.gif\")  
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Write the equation for a parabola with a focus at (5,-5)
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document.write( "and a directrix at y=-4.
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document.write( "Plot the focus (a point) and the directrix (a line):\r\n" );
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document.write( "The vertex is half-way between the focus and the directrix. \r\n" );
document.write( "Halfway between -4 (the distance the directrix is below the \r\n" );
document.write( "x-axis) and -5, the y-coordinate of the focus (4,-5) is the \r\n" );
document.write( "point (4,-4.5) or (4,-9/2).\r\n" );
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document.write( "The equation of such a parabola is \r\n" );
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document.write( "(x-h)² = 4p(y-k) \r\n" );
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document.write( "Where (h,k) = (4,-9/2) and |p| = the distance from the focus \r\n" );
document.write( "to the vertex which is also the distance from the vertex to \r\n" );
document.write( "the directrix. So |p| = 1/2 or 0.5.\r\n" );
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document.write( "If the parabola opens upward p is taken positive and if the \r\n" );
document.write( "parabola opens downward, p is taken negative. The directrix \r\n" );
document.write( "is outside the parabola and the focus is inside the parabola, \r\n" );
document.write( "so the parabola must open downward, so p = -1/2 or -0.5\r\n" );
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document.write( "Substituting\r\n" );
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document.write( "(x-4)² = 4(-1/2)[y-(-9/2)]\r\n" );
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document.write( "(x-4)² = -2(y+9/2) <--equation in standard form:\r\n" );
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document.write( "Edwin \n" );
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