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 is located above the vertex . Both points has the same value...

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 is located above the vertex . Both points has the same value of .

Thus, the parabola opens upward. In this case, we follow the standard formula:  . We consider the following properties:

 vertex as

 focus as

  directrix as

 Note: is the distance of between focus and vertex or distance between directrix and vertex.

From the given vertex point , we determine h =0 and k=0.

From the given focus , we determine and .

Plug-in  on . we get:

Plug-in the values: , , and  on the standard formula, we get:

 as the standard form of the equation of the parabola with vertex and focus .