The answer is simple - however the calculation itself can be involved:
1.) Calcualte the magnitude of the transfer function
2.) Set the magnitude equal to 0.7071 (for 3-dB cutoff) and solve for w.
3.) For Chebyshev and elliptic (Cauer) response: Set the magnitude equal to the value at dc and solve for w.
are you really sure that the above link contains the information you want
(relationship between cut-off and pole frequency for a second order lowpass) ?
Just one additional comment (in case you don't know yet):
The formula gives you the 3-dB cut-off.
However, for Chebyshev and elliptic (Cauer) responses it is common (also) to use another definition for cut-off (end of pass band):
The frequency where the peak (ripple) in the pass band crosses the transfer function value at w=0.
In most textbooks, this definitin is used to table the pole data.