(5/2,0) Write the standard form of the equation of the parabola with the given focus and vertex at (0,0)

A parabola opens toward to the location of focus with respect to the vertex.
When the vertex and focus has same y-values, it implies that the parabola opens sideways (left or right). 
When the vertex and focus has same x-values, it implies that the parabola may opens upward or downward. 
The given focus of the parabola (5/2,0) is located at the right side of the vertex (0,0). Both points has the same value of y=0 .
Thus, the parabola opens sideways towards to the right side of the vertex. In this case, we follow the standard formula: (y-k)^2=4p(x-h). We consider the following properties:
vertex as (h,k)
focus as (h+p, k)
directrix as x=h-p
Note: p is the distance of between focus and vertex or distance between directrix and vertex.
From the given vertex point (0,0) , we determine h =0 and k=0 .
From the given focus (5/2,0) , we determine h+p =5/2 and k=0 .
Applying h=0 on h+p=5/2 , we get:
0+p=5/2
p=5/2 
Plug-in the values: h=0 ,k=0 , and p=5/2 on the standard formula, we get: 
(y-0)^2=4*5/2(x-0) 
y^2=10x  as the standard form of the equation of the parabola with vertex (0,0) and focus (5/2,0) .