Question

Find the standard form of the equation of the parabola with a focus at (3, 0) and a directrix at x = -3.

Answer 1

If we have the directrix at x = -3 (a vertical line) and the focus at (3, 0), then the vertex of the parabola is between these two, at the origin (0, 0). The parabola itself opens in the direction of the focus, which is to the right. The general equation for a parabola opening to the right is x^2 = 4cy, where c is the distance from the vertex to the focus (or to the directrix). In this case, c = 3 (from (0,0) to (3,0)). Therefore, the equation is x^2 = 12y, which is identical to y = (1/12)x^2, choice A.