Final answer:
The equation x = -1 is the correct directrix for the parabola x = 1/4y². The directrix is vertical, and in this case, located to the left of the vertex of the parabola, indicating that the parabola opens to the right. The parabola opens to the right, the directrix is to the left of the vertex, so if the vertex is at (0,0), the directrix would be x = -1, which corresponds to option a).
Step-by-step explanation:
The equation for the directrix of the parabola x = 1/4y² is given as x = -1. This implies that the parabola opens to the right, as the directrix is vertical and located to the left of the vertex. The standard form of a parabola with a vertical directrix is (x - h) = 1/(4p)(y - k)², where (h, k) is the vertex and p is the distance from the vertex to the focus (which is the same as the distance from the vertex to the directrix).
To find the correct equation of the directrix, we can compare this standard form with the given parabola equation. The coefficient 1/4 in x = 1/4y² indicates that the distance p is 1. Since the parabola opens to the right, the directrix is to the left of the vertex, so if the vertex is at (0,0), the directrix would be x = -1, which corresponds to option a).