Question: Solve parametric equations with restriction on parameters

Hello! How can I solve a linear equation which depends on two parameters (a,b) for which the assumption a^2 + b^2 = 1 shall hold. This does not work by writing assume or assuming. The problem has the following form: tau := f(a,b) -> eigenvalues of a matrix U = U(a,b) M := U - tau*Id = M(tau,a,b) = M(a,b) find the kernel of M (eigenvectors of U) and simplify using a^2 + b^2 = 1. I do not want to write down the exact matrix and hope that this information is enough. If not, I will take some time to write it down. Greetings, yadaddy.
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