8. Conic Sections

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

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (x + 1)² = - 8(y + 1)

Find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). (x + 1)² = - 4(y + 1)

a. b. c. d.

Find the vertex, focus, and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). (y - 1)² = 4(x - 1)

a. b. c. d.

In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). x^2 = - 4y

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (y + 1)² = - 8x

Find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d).

a. b. c. d.

y² = 4x

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

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?

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

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (y-2)^2 = -16x

Convert each equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. x² - 2x - 4y + 9 =0

In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equation to one of the graphs that are shown and labeled (a)–(d). x^2 = 4y

Find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (x - 2)² = 8(y - 1)