8. Conic Sections

If a parabola has the focus at $\(\left\)(2,4\(\right\))$ and a directrix line $x=-4$ , find the standard equation for the parabola.

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? y² + 6y - x + 5 = 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

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

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

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. $y^2=16x$

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

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

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 + 6x - 4y + 1 = 0

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. 8x² + 4y = 0

Find the standard form of the equation of each parabola satisfying the given conditions. Focus: (7, 0); Directrix: x = - 7

Find the focus and directrix of the parabola with the given equation. Then graph the parabola. x² = - 16y