document.write( "Question 1190795: Find the equation of the parabola with vertex at (5, 4) and focus (5, 2). \n" ); document.write( "

Algebra.Com's Answer #822510 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The exclamation point in the response from the other tutor suggests that finding the equation using the definition of a parabola is \"THE\" way to solve the problem.

\n" ); document.write( "Very much not so. Finding the equation is much simpler than that.

\n" ); document.write( "The focus is below the vertex, so the parabola opens downward. In vertex form, with vertex (h,k), the equation is

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

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

\n" ); document.write( "We are given vertex (5,4) and p = -2, so the equation is

\n" ); document.write( "ANSWER: $\"y-4=%28-1%2F8%29%28x-5%29%5E2\"$

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