The equation of the parabola whose focus is at (-3, 0) and directrix x = 3 is:

If we plot both the focus and the directrix we get a better idea of what type of parabola this is.  2 things: the parabola will always "hug" the focus, so our parabola is a sideways-opening parabola, opening to the left, to be specific.  Second thing is that the vertex is always halfway between the focus and directrix, on the same axis as the focus.  If the focus has an x value of -3 and the directrix is at x = 3, the halfway mark is at 0.  Since the vertex is on the same axis as the focus, the vertex is (0, 0).  The standard form for a left-opening parabola is .  Our h and k values from the vertex are 0 and 0, so simplifying a bit we have .  Simplifying even further, .  By definition, p is the distance from the vertex to the focus, so our p is 3.  Filling in accordingly, and .  That's the equation for your parabola.

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