Correct. Thats the whole purpose of the private key and thats why you must keep them private (hence the name). The only reason you have the coins in the first place is because you know that secret and can easily make the public key from that secret. Makeing a private key if you only know the public key is very hard (currently considered impossible).
nice!, another question
it's about wallet.dat.
1. What is that?
2. I saw at another thread, once he installed the wallet (e.g Bitcoin Core), he copied it (wallet.dat) to another removable media, then he just delete the OS. why?
3. So wallet.dat is "Removable Wallet"?
Wallet.dat is the file that Bitcoin Core uses to store all the private keys that Bitcoin Core is using, and a list of transactions that were sent to or from that list of Private Keys.
If you remove that file, then you are removing the private keys. If you replace that file you are replacing the private keys. Bitcoin Core also has functionality to add other known private keys to the wallet.dat. This allows you to manipulate the set of addresses that Bitcoin Core has control over.
I use paper wallets for cold storage of bitcoins that I don't expect to spend within the next 3 months, and for providing escrow for transactions.
I use Armory offline for a secure PC based wallet to hold the bitcoins that I think I might want access to during the next 3 months.
I use an android tablet running blockchain.info to hold bitcoins that I expect to spend within the next 48 hours.
If I receive bitcoins while I'm away from home, I use blockchain.info to receive them, and then I transfer them either to an Armory address or a paper wallet when its convenient.