8. Conic Sections

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (- 5, 0); Directrix: x = 5

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, 15); Directrix: y = - 15

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, - 25); Directrix: y = 25

Find the standard form of the equation of each parabola satisfying the given conditions. Vertex: (2, - 3); Focus: (2, - 5)

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (3, 2); Directrix: x = - 1

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (- 3, 4); Directrix: y = 2

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.

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.

In Exercises 31–34, 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)

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

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 graph the parabola. (y + 3)² = 12(x + 1)

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

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

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. y² - 2y + 12x - 35 = 0