document.write( "Question 1170537: The standard form equation of the parabola with focus at (2, 0), directrix y=-3. \n" ); document.write( "

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\n" ); document.write( "Given: the directrix is the line y=-3; the focus is at (2,0).

\n" ); document.write( "With that information, we know the parabola opens upward.

\n" ); document.write( "The distance from the directrix to the focus is 3 (from y=-3 to y=0).

\n" ); document.write( "The vertex is halfway between the directrix and the focus -- at (2,-1.5).

\n" ); document.write( "The vertex form of the equation is

\n" ); document.write( " $\"y+=+%28%281%2F%284p%29%29%28x-h%29%5E2%29%2Bk\"$

\n" ); document.write( "where (h,k) is the vertex and p is the directed distance from the directrix to the vertex, or from the vertex to the focus.

\n" ); document.write( "The given information leads us to a vertex at (2,-1.5) and a p value of 1.5. So the equation is

\n" ); document.write( " $\"y+=+%28%281%2F6%29%28x-2%29%5E2%29-1.5\"$

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