8. Conic Sections

In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function?

$x=-4(y-1{)}^2+3$

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

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. x^2 - 4x - 2y = 0

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.