9. Conic Sections

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

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directrix: x=-12

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). y^2 = 4x

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. y^2 = - 8x

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (7, 0); Directrix: x = - 7

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (- 5, 0); Directrix: x = 5

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (3, 2); Directrix: x = - 1

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (- 3, 4); Directrix: y = 2

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)

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (x + 1)^2 = - 8(y + 1)

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (y + 3)^2 = 12(x + 1)

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (y + 1)^2 = - 8x

In Exercises 43–48, 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. x^2 - 2x - 4y + 9 =0

In Exercises 43–48, 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. y^2 - 2y + 12x - 35 = 0

In Exercises 43–48, 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. x^2 + 6x - 4y + 1 = 0

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

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. (y - 2)^2 = x + 4 y = - (1/2)x

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. x = (y + 2)^2 - 1 (x - 2)^2 + (y + 2)^2 = 1

Identify the conic represented by the equation without completing the square. 4x^2 - 9y^2 - 8x + 12y - 144 = 0

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^2 = 4(y+1)

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. y^2 = 16x

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. 8x^2 + 4y = 0

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Vertex: (2, - 3); Focus: (2, - 5)

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? y = - x^2 + 4x - 3

In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection. Check all solutions in both equations. x = y^2 - 3 x = y^2 - 3y

Identify the conic represented by the equation without completing the square. y^2 + 4x + 2y - 15 = 0

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

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^2 = 4(y+1)

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). y^2 = - 4x

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. y^2 - 6x = 0

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, - 25); Directrix: y = 25

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Vertex: (2, - 3); Focus: (2, - 5)

In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph the parabola. (x - 2)^2 = 8(y - 1)

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? y^2 + 6y - x + 5 = 0

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? y = - x^2 + 4x - 3

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Directrix: y=11

Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. y^2 = 8x

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

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

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. x^2 = - 16y

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, 15); Directrix: y = - 15

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)

In Exercises 49–56, identify each equation without completing the square. y^2 - 4x + 2y + 21 = 0

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Directrix: y=11

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

In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabola. x^2 = 12y

In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, 15); Directrix: y = - 15

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). (x + 1)^2 = - 4(y + 1)