How do we get a matched circuit?

To find a matched circuit, we need to vary the load of a circuit such that a maximum power of the load is obtained.

The matched circuit is given by setting R_L = R_S and X_L = -X_S where R_L is R suffix L representing the load resistance.
The maximum power of the load, P_L = V_S^2 / (4 R_S ).

This is also called conjugate match.