8. Conic Sections

Graph the parabola $-4\left(y+1\right)=\left(x+1\right)^2$, and find the focus point and directrix line.

If a parabola has the focus at $\left(0,-1\right)$ and a directrix line $y=1$, find the standard equation for the parabola.

Graph the parabola $8\left(x+1\right)=\left(y-2\right)^2$ , and find the focus point and directrix line.

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