If a parabola has the focus at $\left(2,4\right)$ and a directrix line $x=-4$ , find the standard equation for the parabola.

• A. $12\left(x+1\right)=\left(y-4\right)^2$
• B. $-\left(x+1\right)=\left(y-4\right)^2$
• C. $12x=y^2$
• D. $4\left(x-1\right)=\left(y+4\right)^2$