#### Answer

The equation for the parabola using the information given is:
$y^{2} = 16x$

#### Work Step by Step

The focus of this parabola is given as $(4, 0)$, so we can see that this parabola has a horizontal axis. We also know that this is a parabola that is not shifted because its vertex is at the origin, so we know that the equation for this parabola with a horizontal axis can be given as:
$y^{2} = 4px$
From the information given, we can see that the value for $p$ is $4$. We can then substitute $4$ for $p$:
$y^{2} = 4(4)x$
We simplify to get the equation for this particular parabola:
$y^{2} = 16x$