8. Conic Sections

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

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

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. y² = - 8x

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

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)

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 = 8x

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. $\(\begin{cases}\)x = (y + 2)^2 - 1 \\(x - 2)^2 + (y + 2)^2 = 1\(\end{cases}\)$

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

Identify each equation without completing the square. y² - 4x + 2y + 21 = 0

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. x² = 12y

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

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.

$\{\begin{array}{c}x=y^2-3\\ x=y^2-3y\end{array}$