document.write( "Question 1175595: Write the standard form of the equation of the parabola with focus at (-2,5) and directrix at x=4. \n" ); document.write( "

Algebra.Com's Answer #801245 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Focus at (-2,5) and directrix at x=4 means the parabola opens to the left.

\n" ); document.write( "The vertex is on the axis of symmetry, halfway between the focus and directrix. Halfway between -2 and 4 is 1, so the vertex is (1,5).

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

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

\n" ); document.write( "or

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

\n" ); document.write( "In that form of the equation, p is the directed distance (i.e., can be negative) from the directrix to the vertex, and from the vertex to the focus. For the given parabola, then, p is -3.

\n" ); document.write( "So we have (h,k) = (1,5) and p = -3; the vertex form of the equation is

\n" ); document.write( " $\"x+=+%28-1%2F12%29%28y-5%29%5E2%2B1\"$

\n" ); document.write( "You can do the conversion of the equation to standard form.

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