Answer: (x - 3)^2 = -24(y + 3)
Explanation:
To find the equation of the parabola in standard form, we can use the formula (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus.
Given that the directrix is y = 3 and the focus is (3, -3), we can see that the parabola opens downward.
The focus is (h, k + p) = (3, -3) and the directrix is y = k - p = 3. By comparing the y-coordinates, we can find p.
-3 = 3 + p
p = -6
Substituting the values into the formula, we get:
(x - 3)^2 = 4(-6)(y - (-3))
So, the equation of the parabola in standard form is (x - 3)^2 = -24(y + 3).