document.write( "Question 1144425: Determine the vertex,focus,endpoints of Latus rectum, directrix and axis of symmetry of the parabola with given equation y^2=4(x-1)
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Algebra.Com's Answer #765567 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The y term is squared, so the parabola opens right or left. Put the given equation in the standard form for a \"horizontal\" parabola:

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

\n" ); document.write( "In that form...
\n" ); document.write( "the vertex is (h,k);
\n" ); document.write( "p is the directed distance from the vertex to the focus, and from the directrix to the vertex; and
\n" ); document.write( "4p is the length of the latus rectum.

\n" ); document.write( " $\"y%5E2+=+4%28x-1%29\"$
\n" ); document.write( " $\"x-1+=+y%5E2%2F4\"$
\n" ); document.write( " $\"x+=+%281%2F4%29%28y-0%29%5E2%2B1\"$

\n" ); document.write( "The vertex is (1,0); p = 1.

\n" ); document.write( "Obviously the axis of symmetry is the horizontal line passing through the vertex.

\n" ); document.write( "Use the vertex and the value of p to find the focus and the directrix;
\n" ); document.write( "then use the focus and the length of the latus rectum to find the endpoints of the latus rectum.
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