Final answer:
The standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = A is y = 5x^2 - 10.
Step-by-step explanation:
The standard form of the equation of a parabola with a focus at (0, -10) and a directrix at y = A can be found using the formula:
y = (1/4a)(x - h)^2 + k
where the vertex of the parabola is at the point (h, k) and the value of a can be determined using the distance between the focus and directrix. In this case, the distance is 20, so a = 1/4 * 20 = 5.
Substituting the values into the formula, we get:
y = (1/4 * 5)(x - 0)^2 + (-10)
y = 5x^2 - 10
Therefore, the standard form of the equation of the parabola is y = 5x^2 - 10.