document.write( "Question 756237: Find the equation for a parabola with its focus at (5, 0) and a directrix of x = -5 \n" ); document.write( "

Algebra.Com's Answer #460050 by josgarithmetic(39620) $\"\"$ $\"About$

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The way the focus and directrix are positioned, this parabola has a minimum. The vertex is directly in the exact middle of focus and directrix, so vertex is (0,0). Without going to derivation process for a parabola equation, you can use $\"x%5E2=4py\"$ , where p is the focal length, same as distance from vertex to the closest point on the directrix.\r
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\n" ); document.write( "\n" ); document.write( "In your question, p=5, and since the parabola has a minimum, the coefficient on $\"x%5E2\"$ is positive (when written in the form y=something...).\r
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\n" ); document.write( "\n" ); document.write( " $\"4py=x%5E2\"$
\n" ); document.write( " $\"y=%281%2F%284p%29%29x%5E2\"$
\n" ); document.write( "and knowing p=5
\n" ); document.write( " $\"y=%281%2F%284%2A5%29%29x%5E2\"$
\n" ); document.write( " $\"highlight%28y=%281%2F20%29x%5E2%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-15%2C15%2C-15%2C15%2C%281%2F20%29x%5E2%29\"$ \n" ); document.write( "

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