8. Conic Sections

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

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 - 3x = y^2 - 3y

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