How to calculate the equivalent conductance of a circuit
The dependent current source doesn't have a resistance itself, but it affects the amount of current entering the circuit as a function of the voltage applied to the circuit.

So, the entire circuit has an effective resistance that depends on the behavior of the dependent current source, specifically the value of \$\beta\$. To see this for yourself, apply some unknown voltage \$V_x\$ to the two terminals on the left and figure out how much current will flow into the top terminal. If you divide the applied voltage by the resulting current you will have the effective resistance.