In addition to the previous responses, I want to add that the Chinese didnt have as much of an incentive to explore the world as the Europeans did. The fall of the Byzantine Empire to the Ottomans resulted in western Europe being cut off from lucrative trade routes that used to be open. This was the main impetus behind Portugal and Spain´s exploration campaigns as they wanted to find a way to circumvent the Ottomans.This is why Columbus was looking for India after all. In short, a big reason why (but not the only one) the new world wasnt conquered by China or the Ottoman Empire is because they really didnt have a pressing economic need to do so because they were already situated along the prime trading routes. China also had a good thing going with their tribute system in which their neighbors were economically subordinate.
Theres an interesting theory that the Confucian principles imbedded in Chinese society may have contributed to restraining the desire for overseas explorations versus the Christian ethos of spreading the gospel but I´m not to well versed in that department.