Posted by Anonymous on Wednesday, April 25, 2012 at 10:04pm.
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?

Algebra: Parabolas  Steve, Wednesday, April 25, 2012 at 11:59pm
Since it's a standard
y^2 = ax, then we know that
16 = 3a
a = 16/3
which makes p = a/4 = 4/3

Algebra: Parabolas  Anonymous, Thursday, April 26, 2012 at 4:49am
So it doesn't matter what point is given as long as it's on the parabola?

Algebra: Parabolas  Steve, Thursday, April 26, 2012 at 10:40am
That's not quite true. They gave the added information that it's a standard parabola with the xaxis 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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