document.write( "Question 1170535: The standard form equation of the parabola with vertex at (4, 1) and directrix x=2. \n" ); document.write( "

Algebra.Com's Answer #795398 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "With the vertex at (4,1) and the directrix the line x=2, the parabola opens to the right. The vertex form of the equation is then

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

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

\n" ); document.write( "We are given (h,k) = (4,1); and p is the distance from the line x=2 to the point (4,1), which is 4-2=2. So p=2 and 4p=8. That gives us all the parts we need to write the equation:

\n" ); document.write( " $\"x+=+%28%281%2F8%29%28y-1%29%5E1%29%2B4\"$

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

\n" );