How to solve a system of non linear equations with non-constant parameters?

I have a system of 2 non_linear (quadratic) equations:

x^2 - 2*a*x + a^2 + y^2 - 2*b*y + b^2 = r^2

x^2 - 2*c*x + c^2 + y^2 - 2*d*y + d^2 = r^2

where x,y are unknowns , and a,b,c,d,r are parameters that change in every iteration inside a loop.

I've tried to use the 'solve()' method , but I get an answer that is a function of the parameters and I need the real number solution.

Answer 1

[Star Strider]

Use matlabFunction to create executable expressions:

syms a b c d r x y

[x, y] = solve(x^2 - 2*a*x + a^2 + y^2 - 2*b*y + b^2 == r^2,  x^2 - 2*c*x + c^2 + y^2 - 2*d*y + d^2 == r^2);

x = simplify(collect(x));
y = simplify(collect(y));

xmf = matlabFunction(x)
ymf = matlabFunction(y)

Then use xmf and ymf (rename them if you want) in your loop.