SOLUTION: 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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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)
Answer by greenestamps(13200) About Me  (Show Source):
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The y term is squared, so the parabola opens right or left. Put the given equation in the standard form for a "horizontal" parabola:

x+=+%281%2F%284p%29%29%28y-k%29%5E2%2Bh

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

y%5E2+=+4%28x-1%29
x-1+=+y%5E2%2F4
x+=+%281%2F4%29%28y-0%29%5E2%2B1

The vertex is (1,0); p = 1.

Obviously the axis of symmetry is the horizontal line passing through the vertex.

Use the vertex and the value of p to find the focus and the directrix;
then use the focus and the length of the latus rectum to find the endpoints of the latus rectum.