MATLAB: Solve: Solution not satisfying the equation

solve

I am trying to solve 2 equations in the code
a = [-0.0008333 -0.025 -0.6667 -20];
length_OnePart = 7.3248;
xi = -6.4446;
yi = -16.5187;
syms x y
[sol_x,sol_y] = solve(y == poly2sym(a), ((x-xi)^2+(y-yi)^2) == length_OnePart^2,x,y,'Real',true);
sol_x = sym2poly(sol_x);
sol_y = sym2poly(sol_y);
The sets of solution it is giving are (-23.9067,-8.7301) and (11.0333,-24.2209) which are not even satisfying the equation of circle. Please help me to rectify the problem.

Best Answer

Sometimes you can reshape the problem to make things easier for the solver. In this case, center the circle at zero by redefining your variables such that: xa=x-xi; ya=y-yi;
a = [-0.0008333 -0.025 -0.6667 -20];
length_OnePart = 7.3248;
xi = -6.4446;
yi = -16.5187;
syms xa ya
[sol_xa,sol_ya] = solve(ya+yi==subs(poly2sym(a),'x',xa+xi), ((xa)^2+(ya)^2) == length_OnePart^2,xa,ya,'Real',true);
sol_x=sol_xa+xi
sol_y=sol_ya+yi
______________________
sol_x =
 -13.182825373861454619370838716408
 0.00002145831413371390464567553686047
sol_y =
 -13.646590348358951818881695033728
 -20.000014306269544436430325843024
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