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)

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) (Show Source): You can put this solution on YOUR website!

The y term is squared, so the parabola opens right or left. Put the given equation in the standard form for a "horizontal" parabola:

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.

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.

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