Question

Which of the following is the equation for a parabola with a focus at (0, -8) and a directrix at y = 8?

a. f(x) = (1/32) ✕ x²
b. f(x) = (1/8) ✕ x²
c. f(x) = -(1/32) ✕ x²
d. f(x) = -(1/8) ✕ x²

Answer 1

The equation for a parabola with a focus at (0, -8) and a directrix at y = 8 is f(x) = (1/32) x².

Step-by-step explanation:

The equation for a parabola with a focus at (0, -8) and a directrix at y = 8 is: f(x) = (1/32) ∙ x² (Option A).

For a parabola with a vertical axis, the standard equation is given by: (x - h)² = 4a(y - k), where (h, k) is the vertex and a is the distance between the vertex and the focus/directrix.

In this case, the vertex is (0, 0) because it lies halfway between the focus and the directrix. So, a = 8 - 0 = 8.

Plugging in the values, we get the equation of the parabola as f(x) = (1/32) ∙ x².