MATLAB Code for Solving Critical Equation

There are some Questions already answered related to circular equations but this is different. There are three circular equations -

(x-a1)^2 + (y-b1)^2 = r1^2 ----------------- (1)

(x-a2)^2 + (y-b2)^2 = r2^2 ----------------- (1)

(x-a3)^2 + (y-b3)^2 = r3^2 ----------------- (1)

Given the values of a1,a2,a3,b1,b2,b3,r1,r2,r3.................

Solve the values for x and y using MATLAB code.

Answer 1

[Roger Stafford]

Those equations are very unlikely to have a solution. You have three equations with only two unknowns to vary. Imagine you have three circles. You are expecting them all to intersect at a common point. That would only happen for special radii and centers. Two circles can intersect at two common points but how likely is it that a third circle would pass through either of these?

[Roger Stafford]

If you have three equations of three spheres in three-dimensional space, that is a problem that could have a solution. In general there will be two solutions if there are any.

[Roger Stafford]

In case it is of interest to you I have written a solution to the problem of finding the intersection points of three spheres in the ninth article of the matlab newsreader thread at:

 http://www.mathworks.com/matlabcentral/newsreader/view_thread/239659