A beam from the focus going directly horizontal should be reflected directly
upward, which means that the parabola at that point has a slope of 1 or -1.
Since the beam is horizontal, it gives us the y-coordinate of the focus.
So...

d/dx (a*x^2+b*x+c) = 2*a*x+b
2*a*x+b = 1    ==>   x = (1-b)/(2*a)
y = a*x^2+b*x+c   ==>   y = (4*a*c-b^2+1)/(4*a)

Similarly with the x-coordinate:

2*a*x+b = 0    ==>   x = -b/(2*a)

So, unless I made a mistake, the focus should be at <-b/(2*a),
(4*a*c-b^2+1)/(4*a)>


David Fontaine wrote:

> You want a parabolic mirror with a light at its focus, like in a
> flashlight. I don't know how to find the focus of a parabola though, Warp
> or somebody?

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