Question 1144425
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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:<br>
{{{x = (1/(4p))(y-k)^2+h}}}<br>
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.<br>
{{{y^2 = 4(x-1)}}}
{{{x-1 = y^2/4}}}
{{{x = (1/4)(y-0)^2+1}}}<br>
The vertex is (1,0); p = 1.<br>
Obviously the axis of symmetry is the horizontal line passing through the vertex.<br>
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.<br>