Algebra: Parabolas

I have a math problem that requires me to find the focal length of a parabola using the information given on a graph. It is a standard horizontal parabola, the formula being y^2 = ax. The focus point is formula a = 4p. I know that a is positive, because the parabola opens right, however I am provided only one point on the parabola, (3, 4). The coordinate of the focus point in not given. Is there any way to solve this?

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  1. Since it's a standard

    y^2 = ax, then we know that

    16 = 3a
    a = 16/3

    which makes p = a/4 = 4/3

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  2. So it doesn't matter what point is given as long as it's on the parabola?

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  3. That's not quite true. They gave the added information that it's a standard parabola with the x-axis as its axis of symmetry, and (0,0) as its vertex.

    In general, knowing only one point on the curve is not enough, but with what they said, you know that you also have (0,0) and (3,-4) as points on the curve.

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