Well you'll need to evolve a dratini. To get a dratini go into the safari park with a super rod...go to the first body of water you see and keep fishing, with a bit of luck you might find it...
go to this link:
http://www.serebii.net/pokearth/kanto/safarizone.shtml
In area one of the safari zone there is a body of water. Fish here with a super rod found in a house on route 12. There is a 70% chance of magikarp, 20% chance of Dratini, and 10% chance of finding Dragonair. Dratini is level 10 and Dragonaire is level 15.
If you want to catch Dratini just throw poke balls and hope that luck is on your side. Otherwise throw 1 rock to make it easier to catch and hope it doesn't flee. If you want to catch Dragonair then you might need to throw 1 rock to have any chance of getting it, but by doing this there is a high chance of it fleeing and still a low chance of you catching it. You need to be really lucky to catch a Dragonair, but you should also just go for Dratini because it is more common and will probably end up stronger since you are training it from a lower level.
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Yes
You can catch dragonair in the dragons den (blackthorn city).
Meowth is not in the wild in Pokemon Yellow. You have to trade to get it
catch it
No you can't catch Mewtwo in Pokemon silver, you must trade it from Pokemon yellow.