Is it true that it takes 6 - 8 week for the knee cap to subside from swelling after arthroscopic surgery?

It's possible: The time for knee effusion to resolve after a knee arthroscopy is highly variable-depends on what was done. It would be unusual if a simple chondroplasty/debridement/menisectomy was done. However, if something more major was done like an acl, microfracture, lateral release, oats procedure this would be within normal limits. Being too active, too early after a scope will cause persistent swelling.