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Original Message (ID '38346') By Bill Simpson:
This is fast with a fairly simple solution. Simplify[Reduce[{ (y1-y0)^2*a^2 == a^2*b^2 - (x1-x0)^2*b^2}, {a, b, x0, y0}]] This slows down with a much bigger solution. Simplify[Reduce[{(y1-y0)^2*a^2 == a^2*b^2 - (x1-x0)^2*b^2, (y2-y0)^2*a^2 == a^2*b^2 - (x2-x0)^2*b^2}, {a, b, x0, y0}]] This takes so long that I give up waiting for it. Simplify[Reduce[{ (y1-y0)^2*a^2 == a^2*b^2 - (x1-x0)^2*b^2, (y2-y0)^2*a^2 == a^2*b^2 - (x2-x0)^2*b^2, (y3-y0)^2*a^2 == a^2*b^2 - (x3-x0)^2*b^2}, {a, b, x0, y0}]] And you can probably guess how much slower and bigger the result might be with four equations. Simplifying equations or getting rid of square roots or denominators before trying to solve, if you are certain that this is valid, will sometimes help speed things up, but not always.