We can find the directrix of a parabola using its standard form (y-k)² = 4p(x-h).
First, we need to identify the values of h, k, and p in the given equation. In the standard form, h and k represent the coordinates of the vertex, and p gives the distance between the vertex and the directrix.
In the equation (y-1)² = -12(x+9), comparing this with the standard form, we can see:
1. The term associated with y is 1, so k is 1.
2. The term associated with x is -9, so h is -9.
3. The coefficient associated with x in the expansion is -12, equated with 4p. So, -12 = 4p -> p = -12/4 = -3.
Now, we have the necessary components to calculate the directrix. For a parabola with a horizontal axis, the formula for the directrix is x = h - p.
Applying these values to our formula, we have x = (-9) - (-3), which simplifies to x = -6.
So, the directrix of the given parabola (y-1)² = -12(x+9) is x = -6.