document.write( "Question 329448: Can you show me how to get the equation of a parabola with a focus (17,9) and a directrix x=12? \n" ); document.write( "

Algebra.Com's Answer #236144 by Edwin McCravy(20059) $\"\"$ $\"About$

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Can you show me how to get the equation of a parabola with a focus (17,9) and a directrix x=12?
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document.write( "The other tutor got the vertex wrong.\r\n" );
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document.write( "Let's draw the directrix line and the vertex:\r\n" );
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document.write( "The vertex is halfway between the focus and the directrix. \r\n" );
document.write( "We draw a green line from the focus to the directrix\r\n" );
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document.write( "That green line is 5 units long, so the midpoint of the green line,\r\n" );
document.write( "which is the vertex, is  units from the directrix and the \r\n" );
document.write( "focus.  So the coordinates of the vertex is (,9) or\r\n" );
document.write( "(,9)\r\n" );
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document.write( "To sketch in the parabola we construct two squares, one on each side of\r\n" );
document.write( "the green line from vertex to focus:\r\n" );
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document.write( "Now we can sketch in the parabola with the vertex and which passes\r\n" );
document.write( "through the corners of those two squares:\r\n" );
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document.write( "The equation of the parabola which opens right or left and has vertex (h,k) \r\n" );
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document.write( "where p is the  or  unit distance between the \r\n" );
document.write( "directrix and the vertex, and also the same distance from the vertex \r\n" );
document.write( "to the focus.  p is taken positive if the parabola opens right, and \r\n" );
document.write( "negative if the parabola opens left.\r\n" );
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document.write( "This parabola opens right so , and with the vertex\r\n" );
document.write( "(h,k) = (,9)\r\n" );
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document.write( "That's the equation of the parabola in standard form.\r\n" );
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document.write( "Edwin

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