document.write( "Question 947097: please i want you to help me find the equation of the locus of points equidistant from the point(0,2) and the straight line y=4. \n" ); document.write( "

Algebra.Com's Answer #797689 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The given conditions are those for a parabola with directrix y=4 and focus (0,2).

\n" ); document.write( "With directrix at y=4 and focus at (0,2), the parabola opens downward. The vertex of the parabola is halfway between the focus and directrix, at (0,3).

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

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

\n" ); document.write( "or

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

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

\n" ); document.write( "The given conditions tell us (h,k) is (0,3) and p is -1. So the equation is

\n" ); document.write( " $\"y+=+%281%2F%284%28-1%29%29%29%28x-0%29%5E2%2B3\"$

\n" ); document.write( "or

\n" ); document.write( " $\"y+=+%28-1%2F4%29x%5E2%2B3\"$

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

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