Tutorial :solving origin of a vectors



Question:

I have two endpoints (xa,ya) and (xb,yb) of two vectors, respectively a and b, originating from a same point (xo, yo). Also, I know that |a|=|b|+s, where s is a constant. I tried to compute the origin (xo, yo) but seem to fail at some point. How to solve this?


Solution:1

Essentially you have two line segments and you know the position of one end for each and their length difference. This easily results in an infinite amount of points where the ends could meet, and therefore doesn't uniquely identify your "origin".


Solution:2

In the general case, there isn't a unique solution. You need another constraint.


Solution:3

The origin will be somewhere on a hyperbolic surface. The points a and b are the foci.


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