document.write( "Question 983231: Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2. \n" ); document.write( "

Algebra.Com's Answer #604026 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the definition of a parabola and the distance formula.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Distance of points (x,y) are equally distant from (0,-2) as from (x,2).
\n" ); document.write( " $\"sqrt%28%28x-0%29%5E2%2B%28y-%28-2%29%29%5E2%29=sqrt%28%28x-x%29%5E2%2B%28y-2%29%5E2%29\"$
\n" ); document.write( " $\"sqrt%28x%5E2%2B%28y%2B2%29%5E2%29=sqrt%280%2B%28y-2%29%5E2%29\"$
\n" ); document.write( " $\"x%5E2%2B%28y%2B2%29%5E2=%28y-2%29%5E2\"$
\n" ); document.write( " $\"x%5E2%2By%5E2%2B4y%2B4=y%5E2-4y%2B4\"$
\n" ); document.write( " $\"x%5E2%2B4y=-4y\"$
\n" ); document.write( " $\"x%5E2=-4y-4y\"$
\n" ); document.write( " $\"-8y=x%5E2\"$ , not yet standard form but useful for understanding the derivation.
\n" ); document.write( " $\"highlight%28y=-%281%2F8%29x%5E2%29\"$ -----standard form.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "That can also be shown as $\"y=-%281%2F8%29%28x-0%29%5E2%2B0\"$ to help show how you can read the standard form equation. Vertex is (h,k) same as (0,0). The parabola has y-axis as its axis of symmetry and the parabola opens downward; the vertex is a maximum point.
\n" ); document.write( " \n" ); document.write( "

\n" );