% function MOBIUS ON CIRCLE
% returns the image of the circle of center c(1) and radius c(2)
% by the Mobius transformation defined by the 2 by 2 matrix matrix M 
% as a circle of center C(1) and radius C(2) 

function C = mobius_on_circle(M,c)
z=c(1)-c(2)^2/conj(M(2,2)/M(2,1)+c(1));
C(1)=mobius(M,z);
C(2)=abs(C(1)-mobius(M,c(1)+c(2)));
end