The equation x^2 = 4py gives 4p = 12, hence p = 3. The focus is at (0, p) = (0, 3).

The standard form of the parabola is x^2 = 4py. Here, 4p = 8, so p = 2. The focus is at (0, p) = (0, 2).

The length of the latus rectum for the parabola y^2 = 4px is given by 4p. Here, p = 4, so the length is 16.

The equation y^2 = -12x can be rewritten as (y - 0)^2 = 4p(x - 0) with p = -3, so the focus is at (-3, 0).

For the parabola y^2 = 4px, here 4p = -8, so p = -2. The directrix is given by x = -p, which is x = 2.

Using the vertex form and substituting the point (2, -4), we find that the equation is y = -2x^2.

The distance from the focus to the directrix is 6, so p = -3. The equation is x^2 = 4py, which gives x^2 = -12y.

The vertex is at (0, 0) and p = 2. The equation is y^2 = 4px, which gives y^2 = 8x.

The vertex form of a parabola is given by (x - h)^2 = 4p(y - k). Here, h = 2, k = 3, and p = 1 (distance from vertex to focus). Thus, the equation is (x - 2)^2 = 4(1)(y - 3) or y = (1/4)(x - 2)^2 + 3.

The equation x^2 = 12y can be rewritten as (y - 0) = (1/3)(x - 0)^2, indicating the focus is at (0, 3).

The standard form of a parabola is y^2 = 4px. Here, 4p = 12, so p = 3. The focus is at (p, 0) = (3, 0).

The length of the latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 16, so p = 4. Therefore, the length of the latus rectum is 4 * 4 = 16.

The vertex of the parabola y^2 = 4px is at (0, 0).

To find the vertex, use x = -b/(2a). Here, a = 1, b = -4, so x = 2. Substitute x = 2 into the equation to find y = -1. Thus, the vertex is (2, -1).

The vertex of the parabola y^2 = 4px is at (0, 0).

The vertex of the parabola y^2 = 4px is at (0, 0). Here, p = 5, but the vertex remains at (0, 0).

Using the vertex form y = a(x - 1)^2 - 2 and substituting (0, 0), we get 0 = a(0 - 1)^2 - 2 => 2 = a => a = 2.

In the equation y^2 = 4px, we have 4p = 16, thus p = 4.

In the equation y^2 = 4px, we have 4p = 20, thus p = 20/4 = 5.

The vertex form of a parabola is given by x = -b/(2a). Here, 1 = -4/(2a) => 2a = -4 => a = -2.

The length of the latus rectum for the parabola x^2 = 4py is given by 4p. Here, 4p = 16, so p = 4. Thus, the length of the latus rectum is 4p = 16.

Since the coefficient of (x - 2)^2 is negative, the parabola opens downwards.

The axis of symmetry for a parabola in the form y^2 = 4px is the x-axis, which is x = 0.

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = -2, b = 4, so x = -4/(2*-2) = 1.

The axis of symmetry for a parabola in the form y = ax^2 + bx + c is given by x = -b/(2a). Here, a = 3 and b = 6, so x = -6/(2*3) = -1.

The standard form of a parabola is (y - k)^2 = 4p(x - h). Here, p = 2, so the directrix is x = -2.

For the parabola y^2 = 4px, here 4p = 8, so p = 2. The directrix is x = -p = -2.

The vertex form of a parabola is y = ax^2. Since it passes through (2, 8), we have 8 = a(2^2) => 8 = 4a => a = 2. Thus, the equation is y = 4x^2.

The distance from the focus to the directrix is 4, so the equation is y = (1/4)(x - 0)^2 + 0, which simplifies to x^2 = 8y.

The distance from the focus to the directrix is 6, so p = 3. The equation is y^2 = 4px = 12y.