Question 1040915
{{{3(x-h)=(y-k)^2}}}
{{{3(x-0)=(y-0)^2}}}
Vertex is (0,0), the Origin.



Compare {{{3(x-0)=(y-0)^2}}}  to  {{{4p(x-0)=(y-0)^2}}}.

p is the distance from vertex to either focus or directrix.  Your parabola is horizontal and the vertex is on the left for minimum x value, and focus is to the right of the vertex.
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{{{4p=3}}}
{{{p=3/4}}}
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The focus is at ( 3/4, 0).



Endpoints of Latus Rectum:
{{{y^2=3x}}}
{{{y=0+- sqrt(3x)}}}
{{{y=0+- sqrt(3(3/4))}}}
{{{y=0+- 3/2}}}


The focus is ON the x-axis;
Latus Rectum is from the upper y-value to the lower y-value at the focus.
{{{(3/2)*2}}}
{{{highlight(LatusRectumLength=3)}}}



Study your book's lesson on this and related, and also study  <a href="https://www.youtube.com/watch?v=M8LGsQMwwj4">derive equation for parabola of given focus and directrix</a>  and <a href="https://www.youtube.com/watch?v=Wworlx39KfQ">same thing, different orientation, but vertex NOT at Origin</a>