document.write( "Question 1173278: Find the equation of the parabola with focus at (8,0) and directrix x=-8 \n" ); document.write( "

Algebra.Com's Answer #798492 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The focus is to the right of the directrix, so the parabola opens to the right. The equation is

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

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

\n" ); document.write( "The vertex is halfway between the directrix and focus, so the vertex is (h,k) = (0,0). That makes p = 8.

\n" ); document.write( "Plug in the values of h, k, and p:

\n" ); document.write( " $\"%28x-0%29+=+%281%2F%284%288%29%29%29%28y-0%29%5E2\"$

\n" ); document.write( " $\"x+=+%281%2F32%29y%5E2\"$

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