where is the downstream o2 sensor located ?

Your Corolla should have a downstream oxygen sensor only if it is equipped to comply with California emissions standards (there is a sticker under the hood which identifies it as either Federal or California). These cars have 2 catalytic converters - the WU-TWC at the exhaust manifold with the upstream O2 sensor threaded into the top of it, and the TWC. The downstream sensor is between the 2 cats, a little closer to the rear cat. The sensor gives information to the computer, which the computer uses to make the engine run efficiently. If the computer is making its decisions based on bad info, it can affect the HC's