Answer:
Focus -> [tex](0,2)[/tex]
Step-by-step explanation:
Because the x-term is squared, the parabola must be vertical.
Recall that the equation for a vertical parabola is [tex]4p(y-k)=(x-h)^2[/tex] where [tex]p[/tex] is the distance from the vertex [tex](h,k)[/tex] to the focus and [tex](h,k+p)[/tex] are the coordinates of the focus.
We can tell by the given equation that the vertex must be located at the origin.
Therefore, we can determine the value of [tex]p[/tex] having known the vertex and the direction of the parabola:
[tex]4p(y-k)=(x-h)^2[/tex]
[tex]4p(y-0)=(x-0)^2[/tex]
[tex]4py=x^2[/tex]
[tex]4py=8y[/tex]
[tex]4p=8[/tex]
[tex]p=2[/tex]
So, given that [tex]p=2[/tex], this means that the coordinates of the focus are [tex](0,2)[/tex].
