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Given two anchor points and a handle point of a cubic Bézier curve, how can I calculate the other handle point in order to make the curve length to a fixed value?

What kind of orbit will it be?

NOTE: Ultimately I will make a solution in C++ for my CAD software. What I need then is, given a point (mouse cursor position), calculate the "nearest" possible handle point that makes the curve to a given length. I assume the orbit should be a closed curve wrapping around the anchor. If that is the case, I would want to check the intersection of a ray (from cursor to the anchor) to the orbit. For performance. I would accept the "nearest" possible point comes from the ray.

Thanks in advance.

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The problem is that the arclength function for a Bézier curve is a rather beastly thing, and thus you're pretty much forced to resort to numerics... –  J. M. Aug 17 '12 at 0:58
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