document.write( "Question 970223: Find the equation for the parabola that has its vertex at the origin and the focal point is 296 units above the directrix. \n" ); document.write( "

Algebra.Com's Answer #592878 by AnlytcPhil(1806) $\"\"$ $\"About$

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Find the equation for the parabola...
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document.write( "Its equation is  \r\n" );
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document.write( " if it opens up or down, \r\n" );
document.write( "with directrix y=k-p and focus (0,k+p) \r\n" );
document.write( "if p is positive it opens up, if p is negative it opens down.\r\n" );
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document.write( "or\r\n" );
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document.write( "{{(x-h)^2}}} if it opens right or left.\r\n" );
document.write( "with directrix x=h-p and focal point (h+p,0)\r\n" );
document.write( "if p is positive it opens right, if negative it opens left.\r\n" );
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\n" ); document.write( "...that has its vertex at the origin
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document.write( "So h=0 and k=0\r\n" );
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document.write( "Its equation is  \r\n" );
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document.write( " if it opens up or down, \r\n" );
document.write( "with directrix y=-p and focus (0,p) \r\n" );
document.write( "if p is positive it opens up, if p is negative it opens down.\r\n" );
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document.write( "or\r\n" );
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document.write( "{{x^2}}} if it opens right or left.\r\n" );
document.write( "with directrix x=-p and focal point (p,0)\r\n" );
document.write( "if p is positive it opens right, if negative it opens left.\r\n" );
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\n" ); document.write( "...and the focal point is 296 units above the directrix.
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document.write( "So it opens upward. The vertex is exactly half-way between the focal point \r\n" );
document.write( "and the directrix line.  The focal point is half of 296 or 148 units above \r\n" );
document.write( "the vertex.  The focal point is (0,148) and the directrix's equation is\r\n" );
document.write( "y = -148, and p=+148 \r\n" );
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document.write( "So its equation is\r\n" );
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document.write( "or \r\n" );
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document.write( "Edwin

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