The parabola has a focus at (−3, 0) and directrix y = 3. what is the correct equation for the parabola? x2 = −12y x2 = 3y y2 = 3x y2 = −12x

The directrix is a straight line that is found at the back of the opening of the parabola with a distance equal to its focal length. So, if the directrix is y = 3, that means that the focal length is 3 and the opening is downwards. The general equation for a parabola opening downwards is:

(x - h)² = -4a(y - k)
where a is the focal length and (h,k) is the vertex

We know a = 3. Now, since focus is at (-3,0) and directrix is at y=3, the middle of -3 and 3 is 0. So, the vertex is at the origin. Therefore, the equation would be:

x² = -12y

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