document.write( "Question 1162872: find the equation of the parabola with the given focus and directrix. focus (5,-2), directrix y=1 \n" ); document.write( "

Algebra.Com's Answer #786811 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "The focus is below the directrix, so the parabola opens downward. The vertex form of the equation of the parabola is

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

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

\n" ); document.write( "The vertex is halfway between the focus and the directrix: (5,-.5). That makes p = -1.5.

\n" ); document.write( "The equation is

\n" ); document.write( " $\"y%2B.5+=%281%2F-6%29%28x-5%29%5E2\"$
\n" ); document.write( " $\"6y%2B3+=+-%28x-5%29%5E2\"$

\n" ); document.write( " \n" ); document.write( "

\n" );